20118Re: 2^m+3^n and 2^n+3^m
- Apr 17, 2009Submitted to OEIS:
Numbers n such that 2^x + 3^y is never prime when max(x,y) = n
1679, 1743, 4980, 4982, 5314, 5513, 5695, 6100, 6578,
7251, 7406, 7642, 8218, 8331, 9475, 9578, 9749
Mark Underwood found that for each non-negative integer n < 1421
there is at least one prime of the form 2^m + 3^n or 2^n + 3^m
with m not exceeding n.
This sequence consists of numbers for which there is no such prime.
David Broadhurst estimated that a fraction in excess of 1/800
of the natural numbers belongs to this sequence and found
17 instances with n < 10^4.
For each of the remaining 9983 non-negative integers n < 10^4,
a prime or probable prime of the form 2^x + 3^y was found with
max(x,y) = n.
Each probable prime was subjected to a combination of
strong Fermat and strong Lucas tests.
David Broadhurst, Apr 17 2009
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