A092245 Lesser of the first twin prime pair with n digits.

3, 11, 101, 1019, 10007, 100151, 1000037, 10000139, 100000037, 1000000007, 10000000277, 100000000817, 1000000000061, 10000000001267, 100000000000097, 1000000000002371, 10000000000001549, 100000000000000019

Offset: 1

Author

Cino Hilliard, Feb 17 2004

Keywords

• base
• nonn

Comments

Sum of reciprocals = 0.43523579465477...

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1000 First 101 from _Abhiram R Devesh_

Crossrefs

Cf. A092250, A124001.

Programs

Maple

for n from 1 to 100 do
  r:= 10^(n-1);
  p:= nextprime(r); q:= nextprime(p);
  while q - p > 2 do
    p:= q; q:= nextprime(p);
  od;
  A[n]:= p;
od:
seq(A[n],n=1..100); # Robert Israel, Aug 04 2014

Mathematica

a[n_] := Block[{p = NextPrime[10^(n -1)]}, While[ !PrimeQ[p +2], p = NextPrime@ p]; p]; Array[a, 18] (* Robert G. Wilson v, Dec 04 2022 *)

PARI

firsttwpr(n) = { sr=0; for(m=0,n, c=0; for(x=10^m+1,10^(m+1), if(isprime(x)&& isprime(x+2),print1(x",");sr+=1./x;break) ) ); print(); print(sr) }

Python

import sympy
for i in range(100):
    p=sympy.nextprime(10**i)
    while not sympy.isprime(p+2):
        p=sympy.nextprime(p)
    print(p)
# Abhiram R Devesh, Aug 02 2014

Formula

a(n) = A124001(n-1) + 10^(n-1). - Robert G. Wilson v, Nov 28 2015

Extensions

Corrected by T. D. Noe, Nov 15 2006