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Numbers k such that 7*10^k + 1 is prime.
7

%I #56 Mar 26 2024 05:32:12

%S 1,2,3,4,5,8,9,45,136,142,158,243,923,1235,2196,4650,6119,7324,9543,

%T 13494,20310,20360,232920,830865,902708,1454508

%N Numbers k such that 7*10^k + 1 is prime.

%C 7*10^902708+1 was the 84th-largest known prime in the world as of Jun 28 2013. Also largest known "base-10" form for a prime number. There are no other values of k in this sequence between 232920 and 902708 that yield a prime. - _Edward A. Trice_, Jul 03 2013

%C Apparently _Edward A. Trice_ found another term in the gap mentioned above in May 2014. - _Ray Chandler_, Apr 29 2015

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/7/70001.htm#prime">Prime numbers of the form 700...001</a>.

%H René-Louis Clerc, <a href="https://ut3-toulouseinp.hal.science/hal-04507547">Nombres S+P, maxSP, minSP et |P-S|</a>, hal-04507547 [math.nt], 2024. (In French)

%H Sabin Tabirca and Kieran Reynolds, <a href="https://web.archive.org/web/20150911144104/http://multimedia.ucc.ie/Staff/ST/articles/SNJ03_Tabirca1.ps">Lacunary Prime Numbers</a>.

%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.

%F a(n) = A101128(n) + 1.

%t Do[ If[ PrimeQ[ 7*10^n + 1], Print[ n ]], {n, 0, 10000}]

%o (PARI) is(n)=ispseudoprime(7*10^n+1) \\ _Charles R Greathouse IV_, Feb 20 2017

%Y Cf. A101128.

%K more,nonn

%O 1,2

%A _Robert G. Wilson v_, Aug 22 2000

%E a(15)-a(20) from _Robert G. Wilson v_, Jan 19 2005

%E a(21)-a(22) from Kamada data by _Robert Price_, Dec 14 2010

%E a(23) from _Edward A. Trice_, Jan 11 2013

%E a(25) (thought to be a(24) at the time) from _Edward A. Trice_, Jun 28 2013

%E a(24) from _Edward A. Trice_, inserted by _Robert G. Wilson v_, May 15 2014

%E a(26) from _Edward A. Trice_, Mar 13 2024