A048895 Bemirps: primes that yield a different prime when turned upside down with reversals of both being two more different primes.

1061, 1091, 1601, 1901, 10061, 10091, 16001, 19001, 106861, 109891, 168601, 198901, 1106881, 1109881, 1606081, 1806061, 1809091, 1886011, 1889011, 1909081, 10806881, 10809881, 11061811, 11091811, 11609681, 11698691, 11816011, 11819011, 11906981

Offset: 1

Author

G. L. Honaker, Jr.

Keywords

• base
• nonn
• nice

Comments

Emirps that yield other emirps when turned upside down. - Lekraj Beedassy, Apr 03 2009

Invertible primes whose reversals are also invertible primes. - Lekraj Beedassy, Apr 04 2009

All terms must begin and end with a one. - T. D. Noe, Apr 21 2014

A term has to include 6 or 9. The concatenation of first n = 809 bemirp 10611091...11688981911 is a prime with 8143 digits being the smallest one for n > 1. There isn't a bemirp < 10^15 with a bemirp index (over all primes). Bemirps such that 4 associated primes are all Sophie Germain primes are 1161880189181, 1191880186181, 1819810881611, 1816810881911, ... . - Metin Sariyar, Mar 06 2020

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..10000 (first 468 terms from T. D. Noe)
• Giovanni Resta, bemirps

Crossrefs

Cf. A003684, A006567, A007628, A046732, A048051, A048052, A048053, A048054.

Programs

Mathematica

upDown[0] = 0; upDown[1] = 1; upDown[6] = 9; upDown[8] = 8; upDown[9] = 6; fQ[p_] := Module[{revP, upDownP, revUpDownP}, If[Intersection[{2, 3, 4, 5, 7}, Union[IntegerDigits[p]]] != {}, False, revP = FromDigits[Reverse[IntegerDigits[p]]]; upDownP = FromDigits[upDown /@ IntegerDigits[p]]; revUpDownP = FromDigits[Reverse[IntegerDigits[upDownP]]]; p != revP && p != upDownP && p != revUpDownP && PrimeQ[revP] && PrimeQ[upDownP] && PrimeQ[revUpDownP]]]; t = {}; nn = 6; Do[p = 10^n; While[p < 2*10^n, p = NextPrime[p]; If[fQ[p], AppendTo[t, p]]], {n, nn}]; t (* T. D. Noe, Apr 21 2014 *)

Extensions

More terms from David W. Wilson