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Seven-digit distinct-digit primes.
14

%I #26 Jun 01 2024 11:37:18

%S 1023467,1023487,1023697,1023769,1023857,1023947,1024357,1024379,

%T 1024579,1024589,1024693,1024697,1024783,1024853,1024957,1024963,

%U 1024987,1025347,1025483,1025693,1025749,1025789,1025839,1025873,1025897,1026359,1026439

%N Seven-digit distinct-digit primes.

%C The last term is a(33950) = 9876413. - _Giovanni Resta_, Mar 19 2013

%C There are 33,950 terms in the sequence. - _Harvey P. Dale_, Jun 01 2024

%H Daniel Starodubtsev, <a href="/A074667/b074667.txt">Table of n, a(n) for n = 1..33950</a> (complete sequence, terms 1..10000 from Nathaniel Johnston)

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

%p 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

%t Select[Range[1023457, 9876543, 2], Length[Union[IntegerDigits[ # ]]]==7 &&PrimeQ[ # ]&]

%t Select[FromDigits/@Permutations[Range[0,9],{7}],IntegerLength[#]==7&&PrimeQ[#]&] (* _Harvey P. Dale_, Jun 01 2024 *)

%o (PARI) is(n)=isprime(n) && #digits(n)==7 && #Set(digits(n))==7 \\ _Charles R Greathouse IV_, Feb 11 2017

%Y The first differences are in A074668.

%Y Cf. A073532 (Number of n-digit primes with all digits distinct). - _Jon E. Schoenfield_, Aug 13 2017

%K fini,full,nonn,base,easy

%O 1,1

%A _Zak Seidov_, Aug 30 2002