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## A big hole in the prime universe

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• Here is a fact: No number of the form 4*b^n+/-1 with b==14mod15 is prime. Does this mean that when b not 14mod15 there is an increased chance of primes and
Message 1 of 2 , Oct 26, 2008
Here is a fact:

No number of the form 4*b^n+/-1 with b==14mod15 is prime.

Does this mean that when b not 14mod15 there is an increased chance of
primes and twins over normal probabilities or are such forms 4*x+/-1,
with x in the form b^n just less prime. My gut feel tells me that the
former is the case.

Regards

Robert Smith
• ... Should have thought more before I posted. All numbers of the stated form are divisible by 3 or 5, so my gut feeling is correct, there is an increased
Message 2 of 2 , Oct 26, 2008
--- In primenumbers@yahoogroups.com, "Robert" <robert_smith44@...> wrote:
>
> Here is a fact:
>
> No number of the form 4*b^n+/-1 with b==14mod15 is prime.
>
> Does this mean that when b not 14mod15 there is an increased chance of
> primes and twins over normal probabilities or are such forms 4*x+/-1,
> with x in the form b^n just less prime. My gut feel tells me that the
> former is the case.
>
> Regards
>
> Robert Smith
>

Should have thought more before I posted. All numbers of the stated
form are divisible by 3 or 5, so my gut feeling is correct, there is
an increased chance that 4*b^n+/-1; b not 14mod15; are prime. It is
just a partial sieve.
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