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A prime nonuplet (Posted on 2017-12-27) Difficulty: 2 of 5
p is a 4-digit prime number. p+30 is also prime. There are 9 primes from p to p+30 inclusive. What is p? What are the 9 primes in the nonuplet?

No Solution Yet Submitted by Math Man    
Rating: 5.0000 (1 votes)

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re(2): computer solution (spoiler) | Comment 3 of 4 |
(In reply to re: computer solution (spoiler) by Jer)

9 primes from p to (p+30) is the max.

An easy way to show this is to realize p=1 or p=-1 mod 6 and to go through the 15 cases for each and eliminate those divisible by 3 or 5.

/////// The statement is correct but the explanation is not.  ///////

I typed too hurriedly.

Mod 30, p can only equal 1,7,11,13,17,19,23,or 29. Whatever the initial value, seven of the 14 values between p and (p+30) can be excluded. 

For example for p=7 mod 30, the values = 9,15,21,25,27,33,35 aren't possible.

Edited on December 28, 2017, 2:59 pm
  Posted by xdog on 2017-12-28 09:26:42

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