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?
(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
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Posted by xdog
on 2017-12-28 09:26:42 |
re(2): computer solution (spoiler)
