A108110 Numbers n such that prime(k)*n+prime(k+1), for k=1,...,6 all are primes.

284, 3074, 3494, 21698, 32138, 43874, 51794, 60674, 75494, 407348, 437438, 459794, 571478, 660878, 667358, 705464, 716624, 740774, 811028, 820154, 910664, 1059398, 1077998, 1122584, 1150748, 1210754, 1222898, 1265018, 1412174, 1461164, 1486574, 1585868, 1631438

Offset: 1

Author

Zak Seidov, Jun 03 2005

Keywords

• nonn

Comments

n == 0 (mod 2). n == 2 (mod 3). n == 3 or 4 (mod 5). - Jason Yuen, Sep 02 2024

Examples

			284 is OK because 2*284+3, 3*284+5, 5*284+7, 7*284+11, 11*284+13 and 13*284+17 all are primes.
		

Crossrefs

Cf. A067076 (k=1), A088879 (k=2), A111224 (k=3), A101123 (k=4), A102721 (k=5).

Cf. A108117 (k=1..7), A379427 (k=1..8).

Programs

Mathematica

s={};Do[If[Union[PrimeQ/@Table[Prime[k]*n+Prime[k+1], {k, 6}]]=={True}, s=Append[s, n]], {n, 2, 1000000, 2}];s

PARI

\\ See isok from A108117
for(n=1,2*10^6,if(isok(n,6),print1(n", "))) \\ Jason Yuen, Sep 02 2024

Extensions

a(22)-a(33) from Jason Yuen, Sep 02 2024