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doctorambientLOL "In this paper we showed how to replicate current quantum factorisation records using first a VIC-20 8-bit home computer from 1981, then an abacus, and finally a dog....[W]e rank a VIC-20 above an abacus, an abacus above a dog, and a dog above a quantum factorisation physics experiment. Finally, we provided standard evaluation criteria for future claimed quantum factorisations."<a href="https://mastodon.social/tags/physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#physics</a> <a href="https://mastodon.social/tags/vic20" class="mention hashtag" rel="nofollow noopener" target="_blank">#vic20</a> <a href="https://mastodon.social/tags/factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#factorization</a> <a href="https://mastodon.social/tags/quantumbullshit" class="mention hashtag" rel="nofollow noopener" target="_blank">#quantumbullshit</a> <a href="https://mastodon.social/tags/quantumcomputing" class="mention hashtag" rel="nofollow noopener" target="_blank">#quantumcomputing</a> <a href="https://mastodon.social/tags/funny" class="mention hashtag" rel="nofollow noopener" target="_blank">#funny</a> <a href="https://mastodon.social/tags/dogs" class="mention hashtag" rel="nofollow noopener" target="_blank">#dogs</a> <a href="https://mastodon.social/tags/abacus" class="mention hashtag" rel="nofollow noopener" target="_blank">#abacus</a><a href="https://eprint.iacr.org/2025/1237.pdf" rel="nofollow noopener" translate="no" target="_blank">https://eprint.iacr.org/2025/1237.pdf</a>

🧿🪬🍄🌈🎮💻🚲🥓🎃💀🏴🛻🇺🇸> Researchers claim to have used a <a href="https://mastodon.social/tags/quantumComputer" class="mention hashtag" rel="nofollow noopener" target="_blank">#quantumComputer</a> to factor a 2,048-bit <a href="https://mastodon.social/tags/RSA" class="mention hashtag" rel="nofollow noopener" target="_blank">#RSA</a> integer.> But the RSA number evaluated was the product of two prime factors that were too close together.> As with a parlor magician's card deck that's been stacked for a card trick> <a href="https://mastodon.social/tags/Quantum" class="mention hashtag" rel="nofollow noopener" target="_blank">#Quantum</a> <a href="https://mastodon.social/tags/factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#factorization</a> is performed using sleight-of-hand numbers that have been selected to make them very easy to factorize using a <a href="https://mastodon.social/tags/physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#physics</a> experiment<a href="https://www.theregister.com/2025/07/17/quantum_cryptanalysis_criticism/" rel="nofollow noopener" translate="no" target="_blank">https://www.theregister.com/2025/07/17/quantum_cryptanalysis_criticism/</a><a href="https://mastodon.social/tags/quantumComputing" class="mention hashtag" rel="nofollow noopener" target="_blank">#quantumComputing</a> <a href="https://mastodon.social/tags/computerScience" class="mention hashtag" rel="nofollow noopener" target="_blank">#computerScience</a> <a href="https://mastodon.social/tags/cryptography" class="mention hashtag" rel="nofollow noopener" target="_blank">#cryptography</a>

DagResearchers Use 1981 Home Computer to Match <a href="https://snabelen.no/tags/Quantum" class="mention hashtag" rel="nofollow noopener" target="_blank">#Quantum</a> <a href="https://snabelen.no/tags/Factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#Factorization</a> Records, Exposing Limitations<a href="https://biggo.com/news/202507131329_Home_Computer_Matches_Quantum_Factorization_Records" rel="nofollow noopener" translate="no" target="_blank">https://biggo.com/news/202507131329_Home_Computer_Matches_Quantum_Factorization_Records</a>

Rémi EismannOne day, one decomposition A000028: Let k = p_1^e_1 p_2^e_2 p_3^e_3 ... be the prime factorization of n. Sequence gives k such that the sum of the numbers of 1's in the binary expansions of e_1, e_2, e_3, ... is odd. 3D graph, threejs - webGL ➡️ <a href="https://decompwlj.com/3Dgraph/A000028.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/3Dgraph/A000028.html</a> 3D graph Gen, threejs animation ➡️ <a href="https://decompwlj.com/3DgraphGen/A000028.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/3DgraphGen/A000028.html</a> 2D graph, first 500 terms ➡️ <a href="https://decompwlj.com/2Dgraph500terms/A000028.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/2Dgraph500terms/A000028.html</a><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#decompwlj</a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathematics</a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener" target="_blank">#sequence</a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#OEIS</a> <a href="https://mathstodon.xyz/tags/javascript" class="mention hashtag" rel="nofollow noopener" target="_blank">#javascript</a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#php</a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#3D</a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#numbers</a> <a href="https://mathstodon.xyz/tags/primes" class="mention hashtag" rel="nofollow noopener" target="_blank">#primes</a> <a href="https://mathstodon.xyz/tags/factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#factorization</a> <a href="https://mathstodon.xyz/tags/PrimeNumbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#PrimeNumbers</a> <a href="https://mathstodon.xyz/tags/binary" class="mention hashtag" rel="nofollow noopener" target="_blank">#binary</a> <a href="https://mathstodon.xyz/tags/expansions" class="mention hashtag" rel="nofollow noopener" target="_blank">#expansions</a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#graph</a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#threejs</a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#webGL</a>

Rémi EismannOne day, one decomposition A276078: Numbers n in whose prime factorization no exponent of any prime(k) exceeds k3D graph, threejs - webGL ➡️ <a href="https://decompwlj.com/3Dgraph/A276078.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/3Dgraph/A276078.html</a> 3D graph Gen, threejs animation ➡️ <a href="https://decompwlj.com/3DgraphGen/A276078.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/3DgraphGen/A276078.html</a> 2D graph, first 500 terms ➡️ <a href="https://decompwlj.com/2Dgraph500terms/A276078.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/2Dgraph500terms/A276078.html</a><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#decompwlj</a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathematics</a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener" target="_blank">#sequence</a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#OEIS</a> <a href="https://mathstodon.xyz/tags/javascript" class="mention hashtag" rel="nofollow noopener" target="_blank">#javascript</a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#php</a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#3D</a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#numbers</a> <a href="https://mathstodon.xyz/tags/factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#factorization</a> <a href="https://mathstodon.xyz/tags/exponent" class="mention hashtag" rel="nofollow noopener" target="_blank">#exponent</a> <a href="https://mathstodon.xyz/tags/primes" class="mention hashtag" rel="nofollow noopener" target="_blank">#primes</a> <a href="https://mathstodon.xyz/tags/PrimeNumbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#PrimeNumbers</a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#graph</a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#threejs</a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#webGL</a>

Rémi EismannOne day, one decomposition A260047: Composites whose prime factorization in base 3 is an anagram of the number in base 33D graph, threejs - webGL ➡️ <a href="https://decompwlj.com/3Dgraph/A260047.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/3Dgraph/A260047.html</a> 3D graph Gen, threejs animation ➡️ <a href="https://decompwlj.com/3DgraphGen/A260047.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/3DgraphGen/A260047.html</a> 2D graph, first 500 terms ➡️ <a href="https://decompwlj.com/2Dgraph500terms/A260047.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/2Dgraph500terms/A260047.html</a><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#decompwlj</a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathematics</a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener" target="_blank">#sequence</a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#OEIS</a> <a href="https://mathstodon.xyz/tags/javascript" class="mention hashtag" rel="nofollow noopener" target="_blank">#javascript</a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#php</a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#3D</a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#numbers</a> <a href="https://mathstodon.xyz/tags/prime" class="mention hashtag" rel="nofollow noopener" target="_blank">#prime</a> <a href="https://mathstodon.xyz/tags/factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#factorization</a> <a href="https://mathstodon.xyz/tags/anagram" class="mention hashtag" rel="nofollow noopener" target="_blank">#anagram</a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#graph</a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#threejs</a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#webGL</a>

Rémi EismannOne day, one decomposition A260046: Composites whose prime factorization in base 2 is an anagram of the number in base 23D graph, threejs - webGL ➡️ <a href="https://decompwlj.com/3Dgraph/A260046.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/3Dgraph/A260046.html</a> 3D graph Gen, threejs animation ➡️ <a href="https://decompwlj.com/3DgraphGen/A260046.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/3DgraphGen/A260046.html</a> 2D graph, first 500 terms ➡️ <a href="https://decompwlj.com/2Dgraph500terms/A260046.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/2Dgraph500terms/A260046.html</a><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#decompwlj</a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathematics</a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener" target="_blank">#sequence</a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#OEIS</a> <a href="https://mathstodon.xyz/tags/javascript" class="mention hashtag" rel="nofollow noopener" target="_blank">#javascript</a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#php</a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#3D</a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#numbers</a> <a href="https://mathstodon.xyz/tags/composites" class="mention hashtag" rel="nofollow noopener" target="_blank">#composites</a> <a href="https://mathstodon.xyz/tags/prime" class="mention hashtag" rel="nofollow noopener" target="_blank">#prime</a> <a href="https://mathstodon.xyz/tags/factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#factorization</a> <a href="https://mathstodon.xyz/tags/anagram" class="mention hashtag" rel="nofollow noopener" target="_blank">#anagram</a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#graph</a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#threejs</a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#webGL</a>

Hacker NewsA first successful factorization of RSA-2048 integer by D-Wave quantum computer<a href="https://www.sciopen.com/article/10.26599/TST.2024.9010028" rel="nofollow noopener" translate="no" target="_blank">https://www.sciopen.com/article/10.26599/TST.2024.9010028</a><a href="https://mastodon.social/tags/HackerNews" class="mention hashtag" rel="nofollow noopener" target="_blank">#HackerNews</a> <a href="https://mastodon.social/tags/quantumcomputing" class="mention hashtag" rel="nofollow noopener" target="_blank">#quantumcomputing</a> <a href="https://mastodon.social/tags/RSA2048" class="mention hashtag" rel="nofollow noopener" target="_blank">#RSA2048</a> <a href="https://mastodon.social/tags/DWave" class="mention hashtag" rel="nofollow noopener" target="_blank">#DWave</a> <a href="https://mastodon.social/tags/factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#factorization</a> <a href="https://mastodon.social/tags/cybersecurity" class="mention hashtag" rel="nofollow noopener" target="_blank">#cybersecurity</a> <a href="https://mastodon.social/tags/technews" class="mention hashtag" rel="nofollow noopener" target="_blank">#technews</a>

Rémi EismannOne day, one decomposition A242414: Numbers whose prime factorization viewed as a tuple of nonzero powers is palindromic3D graph, threejs - webGL ➡️ <a href="https://decompwlj.com/3Dgraph/A242414.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/3Dgraph/A242414.html</a> 2D graph, first 500 terms ➡️ <a href="https://decompwlj.com/2Dgraph500terms/A242414.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/2Dgraph500terms/A242414.html</a><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#decompwlj</a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathematics</a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener" target="_blank">#sequence</a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#OEIS</a> <a href="https://mathstodon.xyz/tags/javascript" class="mention hashtag" rel="nofollow noopener" target="_blank">#javascript</a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#php</a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#3D</a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#numbers</a> <a href="https://mathstodon.xyz/tags/prime" class="mention hashtag" rel="nofollow noopener" target="_blank">#prime</a> <a href="https://mathstodon.xyz/tags/factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#factorization</a> <a href="https://mathstodon.xyz/tags/palindromic" class="mention hashtag" rel="nofollow noopener" target="_blank">#palindromic</a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#graph</a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#threejs</a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#webGL</a>

Rémi EismannOne day, one decomposition A212168: Numbers n such that the maximal exponent in its prime factorization is less than the number of positive exponents (A051903(n) < A001221(n))3D graph, threejs - webGL ➡️ <a href="https://decompwlj.com/3Dgraph/A212168.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/3Dgraph/A212168.html</a> 2D graph, first 500 terms ➡️ <a href="https://decompwlj.com/2Dgraph500terms/A212168.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/2Dgraph500terms/A212168.html</a><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#decompwlj</a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathematics</a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener" target="_blank">#sequence</a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#OEIS</a> <a href="https://mathstodon.xyz/tags/javascript" class="mention hashtag" rel="nofollow noopener" target="_blank">#javascript</a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#php</a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#3D</a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#numbers</a> <a href="https://mathstodon.xyz/tags/exponent" class="mention hashtag" rel="nofollow noopener" target="_blank">#exponent</a> <a href="https://mathstodon.xyz/tags/prime" class="mention hashtag" rel="nofollow noopener" target="_blank">#prime</a> <a href="https://mathstodon.xyz/tags/factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#factorization</a> <a href="https://mathstodon.xyz/tags/PrimeNumbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#PrimeNumbers</a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#graph</a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#threejs</a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#webGL</a>

Rémi EismannOne day, one decomposition A212166: Numbers k such that the maximum exponent in its prime factorization equals the number of positive exponents (A051903(k) = A001221(k))3D graph, threejs - webGL ➡️ <a href="https://decompwlj.com/3Dgraph/A212166.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/3Dgraph/A212166.html</a> 2D graph, first 500 terms ➡️ <a href="https://decompwlj.com/2Dgraph500terms/A212166.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/2Dgraph500terms/A212166.html</a><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#decompwlj</a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathematics</a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener" target="_blank">#sequence</a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#OEIS</a> <a href="https://mathstodon.xyz/tags/javascript" class="mention hashtag" rel="nofollow noopener" target="_blank">#javascript</a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#php</a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#3D</a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#numbers</a> <a href="https://mathstodon.xyz/tags/exponent" class="mention hashtag" rel="nofollow noopener" target="_blank">#exponent</a> <a href="https://mathstodon.xyz/tags/prime" class="mention hashtag" rel="nofollow noopener" target="_blank">#prime</a> <a href="https://mathstodon.xyz/tags/factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#factorization</a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#graph</a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#threejs</a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#webGL</a>

Rémi EismannOne day, one decomposition A212165: Numbers k such that the maximum exponent in its prime factorization is not less than the number of positive exponents (A051903(k) >= A001221(k))3D graph, threejs - webGL ➡️ <a href="https://decompwlj.com/3Dgraph/A212165.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/3Dgraph/A212165.html</a> 2D graph, first 500 terms ➡️ <a href="https://decompwlj.com/2Dgraph500terms/A212165.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/2Dgraph500terms/A212165.html</a><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#decompwlj</a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathematics</a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener" target="_blank">#sequence</a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#OEIS</a> <a href="https://mathstodon.xyz/tags/javascript" class="mention hashtag" rel="nofollow noopener" target="_blank">#javascript</a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#php</a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#3D</a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#numbers</a> <a href="https://mathstodon.xyz/tags/exponent" class="mention hashtag" rel="nofollow noopener" target="_blank">#exponent</a> <a href="https://mathstodon.xyz/tags/prime" class="mention hashtag" rel="nofollow noopener" target="_blank">#prime</a> <a href="https://mathstodon.xyz/tags/factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#factorization</a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#graph</a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#threejs</a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#webGL</a>

Rémi EismannOne day, one decomposition A212164: Numbers k such that the maximum exponent in its prime factorization is greater than the number of positive exponents (A051903(k) > A001221(k))3D graph, threejs - webGL ➡️ <a href="https://decompwlj.com/3Dgraph/A212164.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/3Dgraph/A212164.html</a> 2D graph, first 500 terms ➡️ <a href="https://decompwlj.com/2Dgraph500terms/A212164.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/2Dgraph500terms/A212164.html</a><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#decompwlj</a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathematics</a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener" target="_blank">#sequence</a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#OEIS</a> <a href="https://mathstodon.xyz/tags/javascript" class="mention hashtag" rel="nofollow noopener" target="_blank">#javascript</a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#php</a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#3D</a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#numbers</a> <a href="https://mathstodon.xyz/tags/exponent" class="mention hashtag" rel="nofollow noopener" target="_blank">#exponent</a> <a href="https://mathstodon.xyz/tags/prime" class="mention hashtag" rel="nofollow noopener" target="_blank">#prime</a> <a href="https://mathstodon.xyz/tags/factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#factorization</a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#graph</a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#threejs</a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#webGL</a>

JMLR'Guaranteed Nonconvex Factorization Approach for Tensor Train Recovery', by Zhen Qin, Michael B. Wakin, Zhihui Zhu.<a href="http://jmlr.org/papers/v25/24-0029.html" rel="nofollow noopener" translate="no" target="_blank">http://jmlr.org/papers/v25/24-0029.html</a> <a href="https://sigmoid.social/tags/tensor" class="mention hashtag" rel="nofollow noopener" target="_blank">#tensor</a> <a href="https://sigmoid.social/tags/tensors" class="mention hashtag" rel="nofollow noopener" target="_blank">#tensors</a> <a href="https://sigmoid.social/tags/factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#factorization</a>

Jon AwbreyRiffs and Rotes • Happy New Year 2025 • <a href="https://inquiryintoinquiry.com/2025/01/01/riffs-and-rotes-happy-new-year-2025/" rel="nofollow noopener" translate="no" target="_blank">https://inquiryintoinquiry.com/2025/01/01/riffs-and-rotes-happy-new-year-2025/</a>\( \text{Let} ~ p_n = \text{the} ~ n^\text{th} ~ \text{prime}. \)\( \text{Then} ~ 2025 = 81 \cdot 25 = 3^4 5^2 \)\( = {p_2}^4 {p_3}^2 = {p_2}^{{p_1}^{p_1}} {p_3}^{p_1} = {p_{p_1}}^{{p_1}^{p_1}} {p_{p_2}}^{p_1} = {p_{p_1}}^{{p_1}^{p_1}} {p_{p_{p_1}}}^{p_1} \)No information is lost by dropping the terminal 1s. Thus we may write the following form.\[ 2025 = {p_p}^{p^p} {p_{p_p}}^p \]The article linked below tells how forms of that sort correspond to a family of digraphs called “riffs” and a family of graphs called “rotes”. The riff and rote for 2025 are shown in the next two Figures.Riff 2025 • <a href="https://inquiryintoinquiry.files.wordpress.com/2025/01/riff-2025.png" rel="nofollow noopener" translate="no" target="_blank">https://inquiryintoinquiry.files.wordpress.com/2025/01/riff-2025.png</a>Rote 2025 • <a href="https://inquiryintoinquiry.files.wordpress.com/2025/01/rote-2025.png" rel="nofollow noopener" translate="no" target="_blank">https://inquiryintoinquiry.files.wordpress.com/2025/01/rote-2025.png</a>Reference —Riffs and Rotes • <a href="https://oeis.org/wiki/Riffs_and_Rotes" rel="nofollow noopener" translate="no" target="_blank">https://oeis.org/wiki/Riffs_and_Rotes</a><a href="https://mathstodon.xyz/tags/Arithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#Arithmetic</a> <a href="https://mathstodon.xyz/tags/Combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Combinatorics</a> <a href="https://mathstodon.xyz/tags/Computation" class="mention hashtag" rel="nofollow noopener" target="_blank">#Computation</a> <a href="https://mathstodon.xyz/tags/Factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#Factorization</a> <a href="https://mathstodon.xyz/tags/GraphTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#GraphTheory</a> <a href="https://mathstodon.xyz/tags/GroupTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#GroupTheory</a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener" target="_blank">#Logic</a> <a href="https://mathstodon.xyz/tags/Mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Mathematics</a> <a href="https://mathstodon.xyz/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#NumberTheory</a> <a href="https://mathstodon.xyz/tags/Primes" class="mention hashtag" rel="nofollow noopener" target="_blank">#Primes</a> <a href="https://mathstodon.xyz/tags/Recursion" class="mention hashtag" rel="nofollow noopener" target="_blank">#Recursion</a> <a href="https://mathstodon.xyz/tags/Representation" class="mention hashtag" rel="nofollow noopener" target="_blank">#Representation</a> <a href="https://mathstodon.xyz/tags/RiffsAndRotes" class="mention hashtag" rel="nofollow noopener" target="_blank">#RiffsAndRotes</a>

JMLR'Triple Component Matrix Factorization: Untangling Global, Local, and Noisy Components', by Naichen Shi, Salar Fattahi, Raed Al Kontar.<a href="http://jmlr.org/papers/v25/24-0400.html" rel="nofollow noopener" translate="no" target="_blank">http://jmlr.org/papers/v25/24-0400.html</a> <a href="https://sigmoid.social/tags/minimization" class="mention hashtag" rel="nofollow noopener" target="_blank">#minimization</a> <a href="https://sigmoid.social/tags/factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#factorization</a> <a href="https://sigmoid.social/tags/sparse" class="mention hashtag" rel="nofollow noopener" target="_blank">#sparse</a>

Rémi EismannOne day, one decomposition A130091: Numbers having in their canonical prime factorization mutually distinct exponents3D graph, threejs - webGL ➡️ <a href="https://decompwlj.com/3Dgraph/A130091.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/3Dgraph/A130091.html</a> 2D graph, first 500 terms ➡️ <a href="https://decompwlj.com/2Dgraph500terms/A130091.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/2Dgraph500terms/A130091.html</a><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#decompwlj</a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathematics</a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener" target="_blank">#sequence</a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#OEIS</a> <a href="https://mathstodon.xyz/tags/javascript" class="mention hashtag" rel="nofollow noopener" target="_blank">#javascript</a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#php</a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#3D</a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#numbers</a> <a href="https://mathstodon.xyz/tags/prime" class="mention hashtag" rel="nofollow noopener" target="_blank">#prime</a> <a href="https://mathstodon.xyz/tags/factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#factorization</a> <a href="https://mathstodon.xyz/tags/distinct" class="mention hashtag" rel="nofollow noopener" target="_blank">#distinct</a> <a href="https://mathstodon.xyz/tags/exponents" class="mention hashtag" rel="nofollow noopener" target="_blank">#exponents</a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#graph</a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#threejs</a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#webGL</a>

badkeysI previously helped discover that RSA keys in certificates generated by printers from Canon and Fuji could be factorized with the centuries-old Fermat factorization algorithm <a href="https://fermatattack.secvuln.info/" rel="nofollow noopener" translate="no" target="_blank">https://fermatattack.secvuln.info/</a> <a href="https://infosec.exchange/tags/rsa" class="mention hashtag" rel="nofollow noopener" target="_blank">#rsa</a> <a href="https://infosec.exchange/tags/factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#factorization</a> <a href="https://infosec.exchange/tags/fermat" class="mention hashtag" rel="nofollow noopener" target="_blank">#fermat</a>

Rémi EismannOne day, one decomposition A073493: Numbers having exactly one prime gap in their factorization3D graph, threejs - webGL ➡️ <a href="https://decompwlj.com/3Dgraph/A073493.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/3Dgraph/A073493.html</a> 2D graph, first 500 terms ➡️ <a href="https://decompwlj.com/2Dgraph500terms/A073493.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/2Dgraph500terms/A073493.html</a><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#decompwlj</a> <a href="https://mathstodon.xyz/tags/maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#maths</a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathematics</a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener" target="_blank">#sequence</a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#OEIS</a> <a href="https://mathstodon.xyz/tags/javascript" class="mention hashtag" rel="nofollow noopener" target="_blank">#javascript</a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#php</a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#3D</a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#numbers</a> <a href="https://mathstodon.xyz/tags/prime" class="mention hashtag" rel="nofollow noopener" target="_blank">#prime</a> <a href="https://mathstodon.xyz/tags/gap" class="mention hashtag" rel="nofollow noopener" target="_blank">#gap</a> <a href="https://mathstodon.xyz/tags/factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#factorization</a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#graph</a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#threejs</a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#webGL</a>

Rémi EismannOne day, one decomposition A073492: Numbers having at least one prime gap in their factorization3D graph, threejs - webGL ➡️ <a href="https://decompwlj.com/3Dgraph/A073492.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/3Dgraph/A073492.html</a> 2D graph, first 500 terms ➡️ <a href="https://decompwlj.com/2Dgraph500terms/A073492.html" rel="nofollow noopener" translate="no" target="_blank">https://decompwlj.com/2Dgraph500terms/A073492.html</a><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#decompwlj</a> <a href="https://mathstodon.xyz/tags/maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#maths</a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathematics</a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener" target="_blank">#sequence</a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#OEIS</a> <a href="https://mathstodon.xyz/tags/javascript" class="mention hashtag" rel="nofollow noopener" target="_blank">#javascript</a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#php</a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#3D</a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#numbers</a> <a href="https://mathstodon.xyz/tags/prime" class="mention hashtag" rel="nofollow noopener" target="_blank">#prime</a> <a href="https://mathstodon.xyz/tags/gap" class="mention hashtag" rel="nofollow noopener" target="_blank">#gap</a> <a href="https://mathstodon.xyz/tags/factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#factorization</a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#graph</a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#threejs</a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#webGL</a>

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