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Numbers k such that 101^k-100 is prime.
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%I #32 Jun 08 2024 15:41:27

%S 3,7,9,19,29,99,145,623,3001,6225,23163

%N Numbers k such that 101^k-100 is prime.

%C Related to hyperperfect numbers of a certain form.

%C 101^623-100, a 1249-digit number, has been certified prime with Primo. - _Rick L. Shepherd_, Jun 21 2002

%C a(10) > 6100. - _Michael S. Branicky_, Mar 07 2021

%H J. S. McCranie, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/mccranie.html">A study of hyperperfect numbers</a>, J. Int. Seqs. Vol. 3 (2000) #P00.1.3.

%t Do[ If[ PrimeQ[101^n - 100], Print[n]], {n, 1, 1850}]

%o (PARI) is(n)=ispseudoprime(101^n-100) \\ _Charles R Greathouse IV_, Jun 13 2017

%o (Python)

%o from sympy import isprime

%o def aupto(lim): return [k for k in range(lim+1) if isprime(101**k-100)]

%o print(aupto(625)) # _Michael S. Branicky_, Mar 07 2021

%K nonn,more

%O 1,1

%A _Jud McCranie_

%E Edited and extended by _Robert G. Wilson v_, Jun 18 2002

%E a(9) from _Michael S. Branicky_, Mar 07 2021

%E a(10) from _Michael S. Branicky_, Jan 12 2023

%E a(11) from _Michael S. Branicky_, Jun 08 2024