# Integer Factorisation

If I have a set of numbers of the form $\{ {kp+r}:k\geq0\}$ with p a prime or product of primes k large in $\in Z^+$ and r fixed, is it computationally feasible to find a factorisation for any one of these numbers, supposing p is very large > 1000 bits.

For context, I am thinking whether this variant of the integer factorisation problem is acceptable.

Cheers.

• What is r? Is it different for all numbers? How large is it? How large is k? Are k and r picked uniformly at random? – Geoffroy Couteau Feb 12 '18 at 23:50