A057659 Prime numbers whose square is composed of just two different decimal digits.

5, 7, 11, 109, 173, 81619

Offset: 1

Author

Carlos Rivera, Oct 15 2000

Keywords

• nonn
• base
• more

Comments

Conjectured to be a finite sequence.

No further terms up to prime(1000000)=15485863. - Harvey P. Dale, Mar 20 2011

Examples

			81619^2 = 6661661161.
		

References

• Related to the Unsolved problem F24, p. 262, of the UPiNT by R. K. Guy

Crossrefs

Subsequence of A016069.

Cf. A235154.

Programs

Maple

filter:= p -> nops(convert(convert(p^2,base,10),set))= 2:
select(filter, [seq(ithprime(i),i=1..10^5)]); # Robert Israel, Feb 11 2025

Mathematica

Select[Prime[Range[10000]],Count[DigitCount[#^2],0] ==8&] (* Harvey P. Dale, Mar 20 2011 *)

PARI

select(x->#Set(digits(x^2))==2, primes(10000)) \\ Michel Marcus, Feb 11 2025