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Topic: primes in the arithmetic sequence 1, 31, 61, 91, 121, ... 30k+1 ...
Replies: 4   Last Post: Apr 24, 2013 11:24 AM

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 gnasher729 Posts: 419 Registered: 10/7/06
Re: primes in the arithmetic sequence 1, 31, 61, 91, 121, ... 30k+1 ...
Posted: Apr 22, 2013 2:22 PM
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> I.e. Out of thirteen consecutive integers from the sequence
>       of the 30k+1, can we get at least 12 primes out
>       of the thirteen numbers, for the right choice
>       of the 13 consecutive numbers ?

Of those 13 consecutive numbers, one or two are divisible by 7; one or
two are divisible by 11, one is divisible by 13, at most one divisible
by 17 etc. To have only one divisible by 7, it must be the middle one.
To have only one number composite, that number must also be divisible
by 11 and 13. 1001 = 7x11x13. So you need to check

(1001 * (30k + 11)) - 180, -150, -120, -90, -60, -30, +30, +60,
+90, +120, +150, +180.

389,232,355,162,471 + 0, 30, 60, 90, 120, 150, 210, 240, 270, 300,
330, 360 are all primes.

Date Subject Author
4/22/13 David Bernier
4/22/13 gnasher729
4/24/13 David Bernier
4/24/13 HOPEINCHRIST
4/24/13 HOPEINCHRIST

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