

A159625


Numbers n such that 2^x + 3^y is never prime when max(x,y) = n


3



1679, 1743, 4980, 4982, 5314, 5513, 5695, 6100, 6578, 7251, 7406, 7642, 8218, 8331, 9475, 9578, 9749, 10735
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OFFSET

1,1


COMMENTS

Mark Underwood found that for each nonnegative 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 nonnegative 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.


LINKS

Broadhurst's heuristic in the PrimeNumbers list. [Broken link]
Maximilian Hasler, Mike Oakes, Mark Underwood, David Broadhurst and others, Primes of the form (x+1)^px^p, digest of 22 messages in primenumbers Yahoo group, Apr 5  May 7, 2009. [Cached copy]
Underwood's posting in the PrimeNumbers list
A list of 9983 primes or probable primes for the excluded cases with n < 10^4


EXAMPLE

a(3) = 4980, since there is no prime of the form 2^m + 3^4980 or 2^4980 + 3^m with m < 4981 and 4980 is the third number n such that 2^x + 3^y is never prime when max(x,y) = n.


CROSSREFS



KEYWORD

nonn,more,hard


AUTHOR



EXTENSIONS



STATUS

approved



