A074667 Seven-digit distinct-digit primes.

1023467, 1023487, 1023697, 1023769, 1023857, 1023947, 1024357, 1024379, 1024579, 1024589, 1024693, 1024697, 1024783, 1024853, 1024957, 1024963, 1024987, 1025347, 1025483, 1025693, 1025749, 1025789, 1025839, 1025873, 1025897, 1026359, 1026439

Offset: 1

Author

Zak Seidov, Aug 30 2002

Keywords

• fini
• full
• nonn
• base
• easy

Comments

The last term is a(33950) = 9876413. - Giovanni Resta, Mar 19 2013

There are 33,950 terms in the sequence. - Harvey P. Dale, Jun 01 2024

Examples

			a(1)=1023467 because it is the first (smallest) 7-digit prime with all distinct digits.
		

Links

• Daniel Starodubtsev, Table of n, a(n) for n = 1..33950 (complete sequence, terms 1..10000 from Nathaniel Johnston)

Crossrefs

The first differences are in A074668.

Cf. A073532 (Number of n-digit primes with all digits distinct). - Jon E. Schoenfield, Aug 13 2017

Programs

Maple

lim:=pi(1026439): for n from pi(1000000) to lim do p:=ithprime(n): d:=[op(convert(p, base, 10))]: ddig:=true: for k from 0 to 9 do if(numboccur(k, d)>1)then ddig:=false: break: fi: od: if(ddig)then printf("%d, ", p): fi: od: # Nathaniel Johnston, Jun 22 2011

Mathematica

Select[Range[1023457, 9876543, 2], Length[Union[IntegerDigits[ # ]]]==7 &&PrimeQ[ # ]&]
Select[FromDigits/@Permutations[Range[0,9],{7}],IntegerLength[#]==7&&PrimeQ[#]&] (* Harvey P. Dale, Jun 01 2024 *)

PARI

is(n)=isprime(n) && #digits(n)==7 && #Set(digits(n))==7 \\ Charles R Greathouse IV, Feb 11 2017