The nth row of the following triangle contains smallest set of n primes which form n successive terms of an arithmetic progression from the 2nd to (n+1)th term with the first term 1. 2 2 3 3 5 7 331 661 991 1321 ... Sequence contains the first column.
Conjecture: (1) Sequence is infinite. (2) For every n there are infinitely many arithmetic progressions with n successive primes.
Minimal primes p beginning a chain of n primes in an arithmetic progression of common difference p1.  Robin Garcia, Jun 22 2013
Least prime p such that pi = i*pi+1 is prime for i = 2 to i = n.  Robin Garcia, Jun 22 2013
a(n) is 1 mod 10 for n > 3 because if p is 3 mod 10, then all (2+5*t)*p (1+5*t) for t=0,1,2,... are 5 mod 10; if p is 7 mod 10, all (4+5*t)*p (3+5*t) are 5 mod 10 for t=0,1,2...; if p is 9 mod 10, all (3+5*t)*p  (2+5*t) are 5 mod 10 for t=0,1,2...  Robin Garcia, Jun 22 2013
