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Numbers k where the difference (least prime > 10^k) - (greatest prime < 10^k) sets a record.
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%I #19 Mar 15 2020 13:36:07

%S 1,3,4,9,16,21,24,28,34,66,82,92,117,122,135,218,232,314,387,443,478,

%T 617,652,787,1031,1157,1440,1625,1872,1920,2038,2424,2692,3235,3331,

%U 3798,4944,5202,5241,5938,7572,7847

%N Numbers k where the difference (least prime > 10^k) - (greatest prime < 10^k) sets a record.

%e a(1) = 1: 11 - 7 = 4;

%e a(2) = 3: 1009 - 997 = 12, whereas 101 - 97 = 4 <= a(1).

%o (PARI) d=0;for(k=1,500,my(t=10^k,dd=nextprime(t)-precprime(t));if(dd>d,print1(k,", ");d=dd))

%Y Cf. A003617, A003618, A038804, A331834.

%K nonn,more

%O 1,2

%A _Hugo Pfoertner_, Mar 01 2020

%E More terms from _Jinyuan Wang_, Mar 01 2020

%E a(37)-a(42) from _Giovanni Resta_, Mar 15 2020