2019-10-26 11:20:32 +0200 commented answer Factoring vs Prime identification thank you sir! 2019-10-26 11:19:23 +0200 asked a question Factor function in Sage For factoring large semi-primes (140bit +) is there any GNFS or Msieve in sage? What does factor() use under the hood? 2019-10-07 17:53:27 +0200 received badge ● Student (source) 2019-10-07 17:47:56 +0200 asked a question Factoring vs Prime identification Hey folks, I generated two random primes, using random_prime(2^256) Which gave me: 26743933906960470604491354271488742656120020729367854162490438790852133849203  and 58989902932261902911492570960628926646065206682060380716310751283003413744077  Multiplying them to get a semiprime I get: 1577622065198425994274982187337138762115683359284991921617675178559462773099557341124448864625540436189444788629927033127980383957266963291159527952420631  So maybe this is my miscomprehension, but when I try to run: factor(on the semiprime) -- it takes a long time, never completing. When I run isPrime(on the semiprime) -- it instantly returns false. If indeed sage generates proper primes (non pseudoprimes) how can isPrime be so efficient. Does verifying that a number ISNT prime, not require identifying a factor? If so, why does factorisation take so long? Thanks