A329979 - OEIS

A329979

Prime numbers which can be represented as p^i * q^j - (p + q) where p and q are odd primes and i,j > 0.

%I #21 Feb 23 2020 15:00:46

%S 7,11,19,23,31,37,43,47,53,59,67,71,79,83,101,103,107,127,131,137,139,

%T 149,163,167,179,181,191,199,211,223,229,233,239,251,263,271,283,293,

%U 307,311,331,347,349,359,367,373,379,383,397,419,421,431,439,443,463,467,479,491,499

%N Prime numbers which can be represented as p^i * q^j - (p + q) where p and q are odd primes and i,j > 0.

%C Numbers of this form are an attempt to generalize Mersenne numbers (see link).

%H Craig J. Beisel, <a href="https://math.stackexchange.com/questions/3451929/can-it-be-shown-that-numbers-of-a-certain-form-produce-primes-more-often-than-ex">Can it be shown that numbers of a certain form produce primes more often than expected?</a>, Math StackExchange, November 2019.

%o (PARI) z=[];forprime(a=3,1000, forprime(b=a+2,1000, for(i=1,10, for(j=1,10, y=a+b; x=a^i*b^j-y; if(x<500 && isprime(x) && setsearch(z,x)==0,z=setunion(z,[x])) )))); print(z)

%K nonn

%O 1,1

%A _Craig J. Beisel_, Nov 26 2019