[Guest]

discovered this one myself a few weeks ago and fell in love with it:

if p1 is prime and p1+c is prime, there will be another prime, p2, such that p2+c is also prime, p2+c being at most 2*p1 +c+1. (p1 =/= 2 obviously)

c =2: 3,5; 5,7; 11,13; 17,19; 29,31; 41,43; 59,61; 71,73;

c =4: 3,7; 7,11; 13,17; 19,23; 37,41; 43,47; 67,71;

c =6: 5,11; 7,13; 11,17; 13,19; 23,29; 31,37; 37,43; 41,47;

c =8: 3;11; 5,13; 11,19; 23,31; 29,37; 53,61; 59,67;

c =10: 3,13;7,17;13,23;19,29;31,41;37,47;43,53;

c =12: 5,17; 7,19; 11,23; 17,29; 19,31; 29,41; 31,43; 41,53;

c =14: 3,17; 5,19; 17,31; 23,37; 29,43; 47,61; 53,67;

c =16: 3,19; 7,23; 13,29; 31,47; 37,53; 43,59; 67,83;

[Guest]

edit: p2 +c will generally be at most 2*p1 +c+1, (obviously c = 20 would fail this. p2 will definitely be less.)

[unreality]

Yeah - and even more interesting and simple law with prime numbers - which still has not been proven - is Goldbach's conjecture that every even number above 2 can be written as the sum of two primes.

It's so simple and test-able but somehow defies explanation