A178007 Largest n-digit prime with the most digits equal to 9.

7, 97, 997, 9949, 99991, 999979, 9999991, 99999989, 999999929, 9999999929, 99999999599, 999999999989, 9999999999799, 99999999999959, 999999999999989, 9999999999999199, 99999999999999997, 999999999999999989, 9999999999999999919, 99999999999999999989, 999999999999999999899, 9999999999999999999929

Offset: 1

Author

Lekraj Beedassy, May 17 2010

Keywords

• nonn
• base

Comments

First maximum the number of 9's, then choose the largest.

From Robert Israel, Dec 18 2024: (Start)

This is believed to be different from A241206, as there should be infinitely many n for which there is no n-digit prime with n-1 digits equal to 9. No examples are known; the least such n is greater than 3400. (End)

Links

• Robert Israel, Table of n, a(n) for n = 1..996

Crossrefs

Cf. A037071, A105975, A003618, A241206, A266148.

Programs

Maple

f:= proc(n) local i,j,a,b,x,y;
     x:= 10^n-1;
     for i from 0 to n-1 do
       for a from 1 to 9 do
         y:= x - a*10^i;
         if isprime(y) then return y fi;
     od od;
     for i from 1 to n-1 do
       for a from 1 to 9 do
         for j from 0 to i-1 do
           for b from 1 to 9 do
             y:= x - a*10^i - b*10^j;
             if isprime(y) then return y fi
    od od od od;
    FAIL
end proc:
map(f, [$1..30]); # Robert Israel, Dec 16 2024

Extensions

Corrected and more terms by Robert Israel, Dec 16 2024