1
vote
1answer
33 views

Question on irreducible polynomials and primes.

Consider the polynomial $p(x) = 1+\sum_{i=1}^d a_i x^i$ where $a_i$ is binary and not all $a_i$ are $0$. Is it possible that $p(2^n)$ is prime for all integer $n>-1 ?$
2
votes
1answer
81 views

Is there a sequence of primes whose decimal representations are initial segments of each other?

I.e., is there a sequence of primes whose decimal expansions have the following form: $$a_1,\ a_1a_2,\ a_1a_2a_3,\ a_1a_2a_3a_4, \dots$$ What about with the order of the digits reversed, so each ...
7
votes
2answers
1k views

It it possible to “compress” a list of large numbers using their prime factors?

On a computer I can have integers on arbitrary size thanks to GMP, so it's represented in base 2 in memory. I'm wondering if it's possible in theory to use less memory if I store only prime factors ...