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A114429 Larger of the greatest twin prime pair with n digits.

%I A114429 #32 Aug 01 2024 09:23:14
%S A114429 7,73,883,9931,99991,999961,9999973,99999589,999999193,9999999703,
%T A114429 99999999763,999999999961,9999999998491,99999999999973,
%U A114429 999999999997969,9999999999999643,99999999999998809,999999999999998929
%N A114429 Larger of the greatest twin prime pair with n digits.
%C A114429 Also the denominator of the largest prime over prime fraction less than 10^n.
%H A114429 Abhiram R Devesh, <a href="/A114429/b114429.txt">Table of n, a(n) for n = 1..100</a>
%F A114429 a(n) = A092250(n) + 2. - _M. F. Hasler_, Jan 17 2022
%t A114429 Table[i=1;Until[PrimeQ[10^n-i]&&PrimeQ[10^n-i-2],i++];10^n-i,{n,18}] (* _James C. McMahon_, Jul 31 2024 *)
%o A114429 (Python)
%o A114429 import sympy
%o A114429 for i in range(1,100):
%o A114429     p=sympy.prevprime(10**i)
%o A114429     while not sympy.isprime(p-2):
%o A114429         p=sympy.prevprime(p)
%o A114429     print(p)
%o A114429 # _Abhiram R Devesh_, Aug 02 2014
%o A114429 (PARI)
%o A114429 a(n)=my(p=precprime(10^n)); while(!ispseudoprime(p-2),p=precprime(p-1)); return(p)
%o A114429 vector(50, n, a(n)) \\ _Derek Orr_, Aug 02 2014
%o A114429 (PARI) apply( {A114429(n,p=10^n)=until(2==p-p=precprime(p-1),);p+2}, [1..22]) \\ twice as fast by avoiding additional ispseudoprime(). - _M. F. Hasler_, Jan 17 2022
%o A114429 (Python)
%o A114429 from sympy import prevprime
%o A114429 def a(n):
%o A114429     p = prevprime(10**n); pp = prevprime(p)
%o A114429     while p - pp != 2: p, pp = pp, prevprime(pp)
%o A114429     return p
%o A114429 print([a(n) for n in range(1, 19)]) # _Michael S. Branicky_, Jan 17 2022
%Y A114429 Cf. A092250 (a(n)-2: lesser of the pair).
%K A114429 base,easy,nonn
%O A114429 1,1
%A A114429 _Cino Hilliard_, Feb 13 2006
%E A114429 Corrected by _T. D. Noe_, Nov 15 2006