A couple of years ago, I did a post about the Blum Blum Shub random number generator. I was watching Psych, and bored, so I decided to just make a picture of the random bits generated when I generated two 50 digit primes. Without further ado, or explanation, check it:
There do indeed seem to be very little pattern in it. Although if you knew the two primes that I used, you could generate the value of not just any bit here, but any bit in the future too.
Time for bed.
Ah, but could one recreate the primes from that image alone?
I stared at it for a while, trying to make the words “April Fool” pop out of a random dot stereogram. Instead it looks more like the classic Japanese painting “Tsunami”. Perhaps a bit late in the year.
Your primes are:
2983759823945837594304984948840598737485948749584730049721
and
8573059282710304384729394725029348271834083717394836494843
Right?
Uh, neither of those are primes. My own python implementation of Pollard rho factoring does trial divisions for primes < 1000, and then churns away to find the factorization of the first to be 3, 61, 151, 241, 164291, 789939529603967, and 3452320937986052799454668571981. The second is a bit easier, with factors 31, 28573, 10615249, 301424413, 4100243659 and 737734369141681373149593767. But I did discover a problem, both primes that I used should have been equivalent to 3 mod 4, and neither was.