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Old 2018-03-15, 13:23   #8
Dr Sardonicus
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Feb 2017

3·5·239 Posts

Originally Posted by JeppeSN View Post
I should have said I was interested in odd primes only (and the number 1 is not prime).
There are some large "generalized Fermat" primes listed, e.g. here; these have the forms

a^(2^20) + 1, a^(2^19) + 1, and a^(2^18) + 1.

Of course, they might not be the smallest prime a^(2^k) + b^(2^k) for their exponents.

In looking at smaller exponents, it did occur to me to look at cases

(a^(2^k) + b^(2^k))/2 with a*b odd. I noticed that (3^2 + 1)/2 and (3^4 + 1)/2 were primes, and, since I knew 2^32 + 1 isn't prime, I tried n = (3^32 + 1)/2. Pari's ispseudoprime(n) returned 1...
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