A240604 Primes p with pi(p), pi(2*p), pi(3*p) and pi(4*p) all prime, where pi(x) denotes the number of primes not exceeding x.
10909, 67247, 185869, 408379, 511111, 1297061, 1730461, 1732333, 2135347, 2266079, 2316203, 2978917, 3477737, 4337257, 4495739, 4691849, 6108461, 6407971, 6591163, 7462589, 7909507, 8165039, 8298337, 8948509, 11144083, 11961373, 15019049, 16074059, 16732561, 19316263
Offset: 1
Keywords
Examples
a(1) = 10909 with 10909, pi(10909) = 1327, pi(2*10909) = 2447, pi(3*10909) = 3511 and pi(4*10909) = 4547 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.
Programs
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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}]
Comments