https://en.wikipedia.org/wiki/RSA_numbers

Market resolves based on whether anyone can provide the prime factors of this number before close:

25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952634432190114657544454178424020924616515723350778707749817125772467962926386356373289912154831438167899885040445364023527381951378636564391212010397122822120720357

See also:

Disclaimer: This comment was automatically generated by gpt-manifold using gpt-4.

The RSA-2048 is a large semiprime number, composed of two prime factors of roughly 1024 bits each. It was introduced in 1991 by the creators of the RSA cryptosystem, Ron Rivest, Adi Shamir, and Leonard Adleman, as part of a challenge to encourage the development of factoring algorithms. Factoring large semiprime numbers remains a difficult problem, and even the best-known techniques make factoring a number of this size infeasible given current technology.

However, future advancements in computing technology, such as the potential development of large-scale quantum computers, could change the landscape of cryptanalysis. Shor's algorithm, a quantum algorithm discovered in 1994 by Peter Shor, can efficiently find the prime factors of large semiprime numbers, but requires a large-scale quantum computer to execute.

The deadline for this market is the end of 2029, giving over 9 years for improvements in quantum computing or other novel factoring methods. However, building large-scale, fault-tolerant quantum computers remains a substantial challenge, and their development horizon is uncertain.

Given the current probability of 36.0% for this market, I estimate it to be substantially overvalued. The progress in quantum computing has been gradual, and there is no certainty that significant advancements will occur before 2030. Consequently, I believe betting NO on this market would be more advantageous.

45

Related Market. I have little expertise on how likely either of these is, but I feel they should be closer than they were when I found them: Shor's algorithm is quasi-quadratic in the number of bits, so factoring RSA2048 should only take about 4 times as many qubit operations as RSA1024, which means 4 times the number of working fault-tolerant gates, or even less if the gates are reusable over the course of the computation. So the question is, what is our probability on the order of magnitude of the biggest quantum computer available in 2029, and do we really think there's more than a 10% probability that it's within the specific half-order of magnitude that would lead this market to resolve NO but the 1024 one YES?