A071060 - OEIS

%I #23 Jun 19 2023 09:20:01

%S 7,73,773,7757,77773,777737,7777753,77777377,777777773,7777777577,

%T 77777777573,777777777773,7777777777573,77777777777753,

%U 777777777777773,7777777777777753,77777777777775557,777777777777777737,7777777777777777577,77777777777777777257,777777777777777777773,7777777777777777773533,77777777777777777775353

%N Largest n-digit prime with only prime digits.

%C Terms a(5) through a(23) have been certified prime with Primo.

%H Michael S. Branicky, <a href="/A071060/b071060.txt">Table of n, a(n) for n = 1..1000</a>

%F Conjecture: a(n) ~ floor((7/9) * 10^n). - _Bill McEachen_, Apr 07 2023

%o (Python)

%o from sympy import isprime

%o from itertools import product

%o def a(n): return next(t for t in (int("".join(p)+e) for p in product("7532", repeat=n-1) for e in "73") if isprime(t))

%o print([a(n) for n in range(1, 24)]) # _Michael S. Branicky_, Apr 29 2023

%o (PARI) genit(nstrt=1,cownt=23)={my(arr=List());for(n=nstrt, nstrt+cownt, my(cand=0); for(i=1,n,cand=10*cand+7); if(ispseudoprime(cand)==1, listput(arr,cand);next); for(j=1,+oo,cand=precprime(cand-1); my(v=digits(cand), pass=1); for(ptr=1, #v, my(q=v[ptr]); if(q==2||q==3||q==5||q==7,next);pass=0;break);if(pass>0,break)); listput(arr,cand)); Vec(arr)} \\ _Bill McEachen_, Apr 29 2023

%Y Cf. A069837.

%K base,nonn

%O 1,1

%A _Rick L. Shepherd_, May 26 2002