# Find factor of a numbers of around 3500 bit long, given 1000 such numbers. Each number is product of s*p, p is constant and s is randomly chosen

Given 1000 numbers of form s*p, number are of 3500 bit long. How to factor these numbers? s and p are not necessarily prime numbers. p is constant for all numbers and s is randomly chosen for all 1000 numbers. Again How to solve the same problem when mod of these numbers is provided instead of direct multiplication.

• Note: "a and x" refers to two undefined quantities. Hint: it appears that the simplest strategy in this attack might work. – fgrieu Dec 6 at 17:31
• Is there other algorithms that might work better for this case. – Ram_Giri Dec 7 at 4:24
• The problem at hand can be solved by application of an algorithm codified in writing for 23 centuries. The whole thing requires like 8 lines of Python once the inputs are gathered, and I guess a mere second of runtime. Yes there are slightly "better" variants for some definitions of that, but it is a good start. – fgrieu Dec 7 at 7:06
• Let $a_1 = s_1 p$ and $a_2 = s_2 p$, take $\gcd(a_1,a_2)$. try with some other $a_i$ couples to deduce the $p$. – kelalaka Dec 7 at 9:00
• I'm voting to close this question as off-topic because t does not seem to have anything to do with cryptography. – Maeher Dec 8 at 11:55