On composite-ness of numbers of certain form

Question

If $a\ge750$ is an integer , then is it true that $\bigl(2\times17^{4a+3}\bigr)+1$ cannot be a prime ?

Is that period a multiplication sign? I guess so (seen it enough many times), but that always leaves me wondering? Sorry about the tag see-saw. The only thing I can tell easily is that if $a\equiv1\pmod 3$, then the number is divisible by seven. — Jyrki Lahtonen, Jun 03 '14 at 07:30

Michael Stocker · Answer 1 · 2014-06-03T13:56:07.557

0

$2*17^{4*1497+3}+1$ is prime.

So the answer is very short: No.

Edit: There are some good tools to search for primes. I used these:

edited Jun 03 '14 at 13:56

answered Jun 03 '14 at 12:20

Michael Stocker

2

The begging question : How do you know that ? – Ewan Delanoy Jun 03 '14 at 12:29

1 Answers1