Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
gnasher729

Posts: 417
Registered: 10/7/06
Re: primes in the arithmetic sequence 1, 31, 61, 91, 121, ... 30k+1 ...
Posted: Apr 22, 2013 2:22 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

> 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.



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.