Don't confuse brute forcing 2^65 possibilities with factoring a 2^65 bit semi-prime (n in RSA). I factored a 2^65.4 bit semi-prime using Sagemath on an M1 in m

Don't confuse brute forcing 2^65 possibilities with factoring a 2^65 bit semi-prime (n in RSA). I factored a 2^65.4 bit semi-prime using Sagemath on an M1 in milliseconds. // get two random primes (pretend P, Q) sage: random_prime(2^34) 12697300267 sage: random_prime(2^33) 3962800609 // make a semi-prime (pretend N) sage: 12697300267*3962800609 50316869230723462603 // check length of semi-prime (65-bits) sage: log(50316869230723462603,2).n() 65.4476759618453 // factor it in 18milliseconds. sage: time factor(50316869230723462603) CPU times: user 9.78 ms, sys: 9.07 ms, total: 18.8 ms Wall time: 23.2 ms 2^1024 bit RSA is about 2^80 in bit strength. This example was 2^65 bit RSA, which is negligible in bit-strength.