What are the prime factors of RSA-2048?

320Ṁ125

2100

99%

Other

0.6%

the number itself (it's prime)

0.1%

1 and 251959084756578934940271832400483985714292821262040320277771378360436620207075955562640185258807844069182906412495150821892985591491761845028084891200728449926873928072877767359714183472702618963750149718246911650776133798590957000973

0.1%

This market resolves to the prime factors of 25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952634432190114657544454178424020924616515723350778707749817125772467962926386356373289912154831438167899885040445364023527381951378636564391212010397122822120720357.

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@TomShlomi 1 is not a prime number. If the number itself is prime, then the prime factorization would just be the number itself.

@JoshuaB Oh I know. I was just creating an arbitrary answer to increase the number of traders in this market for https://manifold.markets/IsaacKing/will-any-of-of-my-open-markets-crea

Does it resolve 50/50 to the two prime factors, or is it done in proportion to the size? The prime factors seem to have historically been within around a power of 2 of each other, and it would be a really hilarious skew to have.

I do absolutely adore this market, since any bet here can be easily checked whether it factors RSA-2048, which presumably was the intention.

I'll resolve to the single answer that contains both prime factors. (Spilling over into a comment as needed due to the length limit.) Not gonna split it.

If multiple answers quality, I'll resolve to the first one that was submitted.

(I picked my favorite prime number!)

@placebo_username It's a bet that humans made a mistake somewhere and the number is accidentally a prime itself. Highly unlikely given how many people would have had to fail to notice, but still vastly more likely than any of the ~10^1227 other options.

@IsaacKing There's at least one of the ~10^1227 other options which, after a few seconds of deliberation, I'd deem more likely than accidental primality RSA-2048.

@placebo_username Thus my investment of only one mana

According to Wikipedia, it is known to have exactly two prime factors. Testing for primality is more efficient than computing factorizations, so if it were prime then the challenge would be much easier.