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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