A092250 Lesser of the greatest twin prime pair with n digits.

5, 71, 881, 9929, 99989, 999959, 9999971, 99999587, 999999191, 9999999701, 99999999761, 999999999959, 9999999998489, 99999999999971, 999999999997967, 9999999999999641, 99999999999998807, 999999999999998927

Offset: 1

Author

Cino Hilliard, Feb 17 2004

Keywords

• base
• nonn

Comments

Sum of reciprocals = 0.215331408...

Also the numerator of the largest prime-over-prime fraction less than 1 that is the ratio of two primes both less than 10^n. - Cino Hilliard, Feb 13 2006 [edited by Jon E. Schoenfield, Dec 01 2019]

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1000
• Robert G. Wilson v, Table of n, a(n) for n = 1..1250 (includes terms with more than 1000 digits)

Crossrefs

Cf. A092245.

Cf. A114429(n) = a(n)+2: largest twin prime < 10^n.

Programs

Mathematica

Array[Block[{k = 10^# - 3}, While[! AllTrue[{k, k + 2}, PrimeQ], k -= 2]; k] &, 18]

PARI

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

PARI

apply( {A092250(n,p=10^n)=until(2==p-p=precprime(p-1),);p}, [1..22]) \\ avoids multiple isprime(): much faster! - M. F. Hasler, Jan 17 2022

Python

from sympy import prevprime
def a(n):
    p = prevprime(10**n); pp = prevprime(p)
    while p - pp != 2: p, pp = pp, prevprime(pp)
    return pp
print([a(n) for n in range(1, 19)]) # Michael S. Branicky, Jan 17 2022