OFFSET
1,1
COMMENTS
Conjecture: For any positive integer n, there are infinitely many primes p with pi(k*p) (k = 1,...,n) all prime.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..2280
Zhi-Wei Sun, Problems on combinatorial properties of primes, preprint, arXiv:1402.6641, 2014.
EXAMPLE
a(1) = 10909 with 10909, pi(10909) = 1327, pi(2*10909) = 2447, pi(3*10909) = 3511 and pi(4*10909) = 4547 all prime.
MATHEMATICA
p[j_, k_]:=p[j, k]=PrimeQ[PrimePi[j*Prime[Prime[k]]]]
p[k_]:=p[k]=p[2, k]&&p[3, k]&&p[4, k]
m=0; Do[If[p[k], m=m+1; Print[m, " ", Prime[Prime[k]]]], {k, 1, 95041}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Apr 09 2014
STATUS
approved