A chain of twin primes.
3, 5, 29, 347, 2081, 412037, 9888887, 2076666269, 2155579587221, 3259236335878151, 3226643972519369489, 290397957526743254009, 169011611280564573833237, 80111503746987607996954337, 531139269842527841019807254309
1
We start with p = 3, and take the next value of p to be k*p-1, where k > 1 is the least number that makes k*p-1 and k*p+1 prime.
T. D. Noe, Plot of 100 terms
T. D. Noe, Table of 100 terms
Eric W. Weisstein, MathWorld: Twin Primes
(Mma) p = 3; Join[{p}, Table[k = 1; While[! (PrimeQ[k*p - 1] && PrimeQ[k*p + 1]), k++]; p = k*p - 1; p, {19}]]
Cf. S000305.
nonn
T. D. Noe, Oct 17 2014