## Re: [PrimeNumbers] A prime puzzle for you

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• In a message dated 30/09/02 17:05:38 GMT Daylight Time, ... Correct (of course!), so congrats to David for spotting what was going on. The background is that I
Message 1 of 5 , Sep 30, 2002
In a message dated 30/09/02 17:05:38 GMT Daylight Time,

> The solution is 4722079
>
Correct (of course!), so congrats to David for spotting what was going on.

The background is that I got into investigating this property of the primes
by wondering whether, for those various formulae of the type f(p) = a^p + ...
for which one can show that any prime factor must be of the form q=2*k*p+1,
one might stand a better chance of finding a prime by concentrating searches
on exponents for which the minimum k in this expression was particularly
large, thereby maximising the number of potential factors which did NOT
divide the number. (The above solution has k_min = 117, no less!)

So I chose 1163 (another "good" one) as exponent and very quickly found the
PRP
401200895^1163-401200894^1163
which I submitted to Henri's database a couple of days ago.

However, by examining the k_min values of the Mersenne exponents, and a
couple of other examples, it appears that this optimism is unfortunately
unfounded.

Unless others can counter this conclusion?

Mike

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