# 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