A071060 Largest n-digit prime with only prime digits.

7, 73, 773, 7757, 77773, 777737, 7777753, 77777377, 777777773, 7777777577, 77777777573, 777777777773, 7777777777573, 77777777777753, 777777777777773, 7777777777777753, 77777777777775557, 777777777777777737, 7777777777777777577, 77777777777777777257, 777777777777777777773, 7777777777777777773533, 77777777777777777775353

Offset

1,1

Comments

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

Links

Michael S. Branicky, Table of n, a(n) for n = 1..1000

Formula

Conjecture: a(n) ~ floor((7/9) * 10^n). - Bill McEachen, Apr 07 2023

Prog

(Python)
from sympy import isprime
from itertools import product
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))
print([a(n) for n in range(1, 24)]) # Michael S. Branicky, Apr 29 2023
(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

Crossrefs

Cf. A069837.

Sequence in context: A113033 A093675 A121127 * A092444 A099141 A084768

Adjacent sequences: A071057 A071058 A071059 * A071061 A071062 A071063

Keyword

base,nonn

Author

Rick L. Shepherd, May 26 2002

Status

approved