A216310 The prime ending in 3 is the only prime in a decade.

113, 293, 683, 743, 773, 863, 953, 983, 1163, 1193, 1373, 1523, 1583, 1733, 1823, 1913, 2003, 2053, 2153, 2213, 2243, 2273, 2423, 2503, 2633, 2663, 2753, 2843, 3023, 3413, 3433, 3593, 3623, 3643, 3803, 3833, 3863, 4363, 4373, 4463, 4493, 4523, 4583, 4603

Offset: 1

Author

V. Raman, Sep 03 2012

Keywords

• nonn
• base
• easy

Comments

Primes of the form 10n+3 such that 10n+1, 10n+7, and 10n+9 are composite. - Charles R Greathouse IV, Sep 06 2012

Links

• V. Raman, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A030431. Cf. A032352, A007811, A078494.

Programs

Mathematica

t = {}; Do[ps = Select[Range[10*n, 10*n + 9], PrimeQ]; If[ps == {10*n + 3}, AppendTo[t, ps[[1]]]], {n, 0, 595}]; t (* T. D. Noe, Sep 04 2012 *)
Select[10*Range[500]+3,PrimeQ[#]&&AllTrue[#+{-2,4,6},CompositeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 27 2016 *)

Formula

a(n) ~ 4n log n. - Charles R Greathouse IV, Sep 06 2012