"Sexy" Primes
A Sexy Prime Sequence is give by a arithmetical progression of primes numbers adding 6, and all terms of this A.P are primes.:
P is a prime number and P+6, P+12... are all prime numbers.
In other words you can make sequences of primes numbers, adding 6 and get new primes.
We can have 2 terms sequences: (11,17) (5,11). Three terms sequences (5, 11, 17) (11, 17, 23), etc.
How large can be one sequence of Sexy Primes?
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1 solution
Prime p° is congruent with x (mod 5) (It means that p/5=5 k+x) and every time we add 6 , we add 1 in mod 5 (6=5 1+1), when we reach pn that is congruent to 5 (mod 5) it is also congruent to 0 (mod 5), it means its equal 5 k, so the larger sequence is when the p1=0(mod5), p2=1(mod5),p3=2(mod5),p4=3(mod5),p5=4(mod5). And that is 5,11,17,23,29 because the only prime=0(mod 5) is 5, otherwise, its 5 k, so its not a prime.