A108312 -id:A108312 - cp's OEIS frontend

A135119 Integers n such that 10^n+57 is a prime number.

1, 2, 5, 11, 22, 30, 31, 43, 44, 64, 107, 191, 2149, 3174, 4952, 12126, 29884, 32645, 48442, 60959, 62750, 87408, 95326

Offset: 1

Julien Peter Benney (jpbenney(AT)gmail.com), Feb 12 2008

See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "10057".

No additional terms <100000.

			5 is a member because 10^5+57 = 100000+57 = 100057, which is a prime number.

Makoto Kamada, List of near-repdigit-related prime numbers.
Index entries for primes involving repunits.

Cf. A095688, A108052, A108050, A108312, A107083, A108049, A108054.

Four PRP terms from Sean A. Irvine, Nov 11 2009
Added term 60959. Robert Price, Mar 22 2010
Added terms 29884,32645. Robert Price, Aug 24 2010
Edited by Ray Chandler, Dec 23 2010
a(19)=48442 from Robert Price, Dec 31 2010
a(21)=62750 from Robert Price, Jan 29 2011
a(22)=87408 from Robert Price, Mar 03 2011
a(23)=95326 from Robert Price, Mar 24 2011
Deleted superseded comment. - Harvey P. Dale, Apr 23 2022

A135131 Integers n such that 10^n + 79 is a prime number.

Original entry on oeis.org

1, 2, 4, 7, 16, 18, 43, 60, 73, 91, 106, 115, 120, 169, 394, 444, 516, 835, 886, 1912, 3120, 3602, 5664, 10188, 14434, 16564, 23732, 29058, 47728, 63916

Offset: 1

Julien Peter Benney (jpbenney(AT)gmail.com), Feb 12 2008

If any additional terms exist, they are >40000. - Robert Price, Sep 25 2010

See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "10079".

			7 is a member because 10^7+79 = 10000000+79 = 10000079, which is a prime number.

Makoto Kamada, List of near-repdigit-related prime numbers.
Index entries for primes involving repunits.

Cf. A095688, A108052, A108050, A108312, A107083, A108049, A108054.

Select[Range[1000], PrimeQ[10^# + 79] &] (* G. C. Greubel, Sep 28 2016 *)

Added two terms: 10188 and 14434. Robert Price, Mar 22 2010
Added seven terms: 1912, 3120, 3602, 5664, 16564, 23732, 29058. Robert Price, Sep 25 2010
Edited by Ray Chandler, Dec 23 2010
a(29)=47728 from Robert Price, Dec 31 2010
a(30)=63916 from Robert Price, Jan 29 2011

A135132 Integers n such that 10^n + 73 is a prime number.

Original entry on oeis.org

1, 2, 8, 11, 145, 695, 1099, 3518, 6211, 13015

Offset: 1

Julien Peter Benney (jpbenney(AT)gmail.com), Feb 12 2008

a(5) to a(7) were certified prime with PRIMO. - Bernardo Boncompagni, Nov 07 2008
The next term (if one exists) is > 100000. - Robert Price, Apr 25 2011
See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "10073".

			8 is a member because 10^8+73 = 100000000+73 = 100000073, which is prime.

Makoto Kamada, List of near-repdigit-related prime numbers.
Index entries for primes involving repunits.

Cf. A095688, A108052, A108050, A108312, A107083, A108049, A108054.

Select[Range[1000], PrimeQ[10^# + 73] &] (* G. C. Greubel, Sep 28 2016 *)

a(7) from Bernardo Boncompagni, Nov 07 2008
Added term 13015. Robert Price, Mar 22 2010
Added two terms: 3518,6211. Robert Price, Oct 10 2010
Edited by Ray Chandler, Dec 23 2010

A258932 Numbers k such that 10^k + 103 is prime.

Original entry on oeis.org

1, 3, 4, 5, 7, 9, 10, 11, 27, 35, 85, 169, 209, 221, 321, 347, 603, 610, 1229, 1391, 2171, 2303, 2679, 3977, 4545, 5721, 7090, 35877

Offset: 1

Vincenzo Librandi, Jun 15 2015

a(29) > 60000. - Michael S. Branicky, Apr 27 2025

			For n = 3, a(3) = 10^3 + 103 = 1103, which is prime.

Sequences of the type 10^n+k: A049054 (k=3), A088274 (k=7), A088275 (k=9), A095688 (k=13), A108052 (k=19), A108050 (k=21), A108312 (k=27), A107083 (k=31), A107084 (k=33), A135109 (k=37), A135108 (k=39), A108049 (k=43), A108054 (k=49), A135118 (k=51), A135119 (k=57), A135116 (k=61), A135115 (k=63), A135113 (k=67), A135114 (k=69), A135132 (k=73), A135131 (k=79), A137848 (k=81), A135117 (k=87), A110918 (k=91), A135112 (k=93), A135107 (k=97), A110980 (k=99), this sequence (k=103), A258933 (k=109), A165508 (k=111), A248349 (k=123456789), A248351 (k=987654321).

[n: n in [1..600] | IsPrime(10^n+103)];

Select[Range[5000], PrimeQ[10^# + 103] &]

is(n)=ispseudoprime(10^n+103) \\ Charles R Greathouse IV, Jun 13 2017

a(26)-a(28) from Jens Kruse Andersen, Jun 23 2015

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A135119 Integers n such that 10^n+57 is a prime number.

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A135131 Integers n such that 10^n + 79 is a prime number.

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A135132 Integers n such that 10^n + 73 is a prime number.

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A258932 Numbers k such that 10^k + 103 is prime.

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