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

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`%I #21 Feb 23 2020 15:00:46
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`%S 7,11,19,23,31,37,43,47,53,59,67,71,79,83,101,103,107,127,131,137,139,
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`%T 149,163,167,179,181,191,199,211,223,229,233,239,251,263,271,283,293,
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`%U 307,311,331,347,349,359,367,373,379,383,397,419,421,431,439,443,463,467,479,491,499
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`%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.
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`%C Numbers of this form are an attempt to generalize Mersenne numbers (see link).
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`%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.
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`%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)
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`%K nonn
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`%O 1,1
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`%A _Craig J. Beisel_, Nov 26 2019
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