A088275 -id:A088275 - cp's OEIS frontend

A108050 Integers k such that 10^k+21 is prime.

1, 3, 9, 17, 55, 77, 133, 195, 357, 1537, 2629, 3409, 8007, 25671, 48003, 55811, 94983, 109615, 135669

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Jun 01 2005

There cannot be any primes of this form when k is even, because all such numbers must be divisible by 11. A number is divisible by 11 if the difference between the sum of its odd digits and the sum of its even digits is 0 or divisible by 11. When k is even, the difference is always 0. - Dmitry Kamenetsky, Jul 12 2008
The next term, if one exists, is >100000. - Robert Price, Mar 24 2011
See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "10021".

			For k=3 we have 10^3+21 = 1000+21 = 1021, which is prime.

Makoto Kamada, List of near-repdigit-related prime numbers
Henri Lifchitz and Renaud Lifchitz (Editors), Search for 10^k+21, PRP Top Records.
Index entries for primes involving repunits

Cf. A049054, A088274, A088275, A138861.

q=21; s=""; For[ a=q,a<=q,s="10^n+"<>ToString[ a ]<>":"; n=0; For[ i=1,i< 10^3,If[ PrimeQ[ 10^i+a ],n=1; s=s<>ToString[ i ]<>"," ]; i++ ]; If[ n>0,Print[ s ] ]; a++ ] (* Vladimir Joseph Stephan Orlovsky, May 06 2008 *)

for(n=1,1e4,if(ispseudoprime(10^n+21),print1(n", "))) \\ Charles R Greathouse IV, Jul 20 2011

a(6)=77 inserted by Vladimir Joseph Stephan Orlovsky, May 06 2008
a(13)=8007 from Dmitry Kamenetsky, Jul 12 2008
a(14)=25671 from Robert Price, Nov 08 2010
Edited by Ray Chandler, Dec 24 2010
a(15)=48003 from Robert Price, Dec 31 2010
a(16)=55811 from Robert Price, Jan 09 2011
a(17)=94983 from Robert Price, Mar 24 2011
a(18)=109615 from Lelio R Paula, added by Boyan Hu, Jul 05 2025
a(19)=135669 from Boyan Hu, Jul 05 2025

A108049 Integers k such that 10^k + 43 is a prime number.

Original entry on oeis.org

1, 5, 37, 253, 1129, 1441, 35393

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Jun 01 2005

a(8) > 10^5. - Robert Price, Nov 01 2013

See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "10043".

			k=5 is a term because 10^5 + 43 = 100043, which is prime.

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

Cf. A049054, A088274, A088275.

Select[Range[2*10^3],PrimeQ[10^#+43]&] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)

is(n)=ispseudoprime(10^n+43) \\ Charles R Greathouse IV, Apr 28 2015

a(7)=35393 from Robert Price, Mar 16 2010

Edited by Ray Chandler, Dec 23 2010

A108052 Integers k such that 10^k+19 is a prime number.

Original entry on oeis.org

1, 3, 5, 7, 10, 11, 17, 59, 81, 108, 574, 629, 1069, 1759, 2063, 2682, 9174, 40929, 42457, 66033

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Jun 01 2005

Verified terms through 9174. - Robert Price, May 24 2010
See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "10019".
No other terms <= 100,000. - Robert Price, Mar 03 2011

			n = 7 we have 10^7+19 = 10000000+19 = 10000019, which is prime.

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

Cf. A049054, A088274, A088275, A095688.

Select[Range[2*10^3],PrimeQ[10^#+19]&] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)

is(n)=ispseudoprime(10^n+19) \\ Charles R Greathouse IV, Apr 28 2015

a(17)=9174 from Ryan Propper, Jan 02 2008
Edited by Ray Chandler, Dec 23 2010
a(18)=40929 and a(19)=42457 from Robert Price, Dec 27 2010
a(20)=66033 from Robert Price, Jan 09 2011

A108054 Integers k such that 10^k+49 is prime.

Original entry on oeis.org

1, 2, 3, 5, 8, 17, 24, 32, 65, 66, 67, 79, 83, 98, 152, 260, 781, 1225, 1777, 2023, 2411, 3469, 5347, 10646, 11335, 13989, 14792, 16731, 19015, 29471, 39187, 41456, 80883, 102824, 154359, 216950, 294475

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Jun 02 2005

See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "10049".

a(38) > 3*10^5. Robert Price, Jul 10 2023

			k = 8 ==> 10^8+49 = 100000049, which is prime.

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

Cf. A049054, A088274, A088275, A095688.

a={};Do[p=10^n+49;If[PrimeQ[p],AppendTo[a,n]],{n,0,10^3,1}];a (* Vladimir Joseph Stephan Orlovsky, Jul 17 2008 *)

for(n=1,1e4,if(ispseudoprime(10^n+49),print1(n", "))) \\ Charles R Greathouse IV, Jul 25 2011

a(23) from Ray G. Opao, Dec 13 2006
a(24)-a(31) from Robert Price, May 28 2010
Edited by Ray Chandler, Dec 23 2010
a(32) from Robert Price, Dec 27 2010
a(33) from Robert Price, Mar 03 2011
a(34)-a(37) from Robert Price, Jul 10 2023

A107083 Integers k such that 10^k + 31 is prime.

Original entry on oeis.org

1, 2, 3, 14, 18, 44, 54, 89, 469, 2060, 2985, 6197, 16452, 19393, 21205, 49657, 74670, 76374

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Jun 08 2005

The next term, if one exists, is >100000. - Robert Price, Apr 26 2011

See Kamada link - primecount.txt for terms, primesize.txt for discovery details including proofs of primality - search on "10031".

			For k = 3 we get 10^3 + 31 = 1000 + 31 = 1031, which is prime.

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

Cf. A049054, A088274, A088275, A095688, A108052, A108050, A108049, A108054.

a={}; Do[If[PrimeQ[p=10^n+31], AppendTo[a, n]], {n, 0, 6*10^2}]; a (* Vladimir Joseph Stephan Orlovsky, Aug 07 2008 *)

16452 and 19393 from Robert Price, Mar 22 2010
Additional term (21205) from Robert Price, May 24 2010
Missing term (6197) added by Robert Price, Dec 07 2010
Edited by Ray Chandler, Dec 23 2010
a(16)=49657 from Robert Price, Dec 31 2010
a(17)=74670 from Robert Price, Jan 29 2011
a(18)=76374 from Robert Price, Mar 03 2011

A088274 Numbers k such that 10^k + 7 is prime.

Original entry on oeis.org

1, 2, 4, 8, 9, 24, 60, 110, 134, 222, 412, 700, 999, 1383, 5076, 5543, 6344, 14600, 15093, 21717, 23636, 30221, 50711, 221628, 350071, 371696, 487291, 995256, 1043372

Offset: 1

Amarnath Murthy, Sep 28 2003

No other terms less than 59500.
No other terms <= 100000. - Robert Price, Mar 03 2011
a(28) > 500000. - Alfred Reich, Jun 10 2021
a(29) > 1000000. - Alfred Reich, Nov 20 2021
a(30) > 1075000. - Alfred Reich, Jan 10 2022

			8 is a term since 10^8 + 7 = 100000007 is a prime.

G. L. Honaker, Jr. and Chris Caldwell, eds., Prime Curios!
Makoto Kamada, Prime numbers of the form 100...007.
Alfred Reich, ProofFile.
Alfred Reich, ProofFile2.
Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers.

Cf. A088275, A049054, A102007, A159031.

Do[ If[ PrimeQ[ 10^n + 7], Print[n]], {n, 0, 10000}] (* Robert G. Wilson v, Dec 16 2004 *)

is(n)=isprime(10^n + 7) \\ Charles R Greathouse IV, Apr 29 2015

a(n) = A102007(n) + 1.

a(7)-a(14) from Ray Chandler, Oct 09 2003
a(15)-a(19) from Robert G. Wilson v, Jan 18 2005
Corrected and extended by Jason Earls, Nov 27 2007 and Dec 07 2007. (14600 was missing and 23636 and 50711 are new. These are presently only probable primes, found with WinPFGW.)
Missing term 30221 added by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
a(24)-a(27) from Alfred Reich, Jun 10 2021
a(28) from Alfred Reich, Nov 20 2021
a(29) from Alfred Reich, Jan 10 2022

A108312 Integers n such that 10^n + 27 is prime.

Original entry on oeis.org

1, 2, 83, 167, 242, 14081, 65537

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Jun 29 2005

The next term, if one exists, is >100000. - Robert Price, May 24 2010

See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "10027".

			For n=2 we have 10^2 + 27 = 100 + 27 = 127, which is prime.

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

Cf. A049054, A088274, A088275, A095688, A107083, A108049, A108050, A108052, A108054.

Do[ If[ PrimeQ[10^n + 27], Print[n]], {n, 3000}] (* Robert G. Wilson v, Jul 01 2005 *)

a(6)=14081 from Robert Price, Mar 22 2010
Edited by Ray Chandler, Dec 23 2010
a(7)=65537 from Robert Price, Jan 29 2011

A110980 Integers n such that 10^n+99 is prime.

Original entry on oeis.org

1, 2, 4, 6, 13, 14, 16, 17, 19, 30, 31, 60, 68, 73, 113, 144, 276, 288, 364, 449, 473, 739, 833, 1171, 1732, 2292, 3912, 7673, 9458, 16982, 19751, 21479, 23837, 77726

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Sep 30 2005

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 "10w99".

			If n=6, we have 10^6+99 = 1000000+99 = 1000099, which is prime.

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

Cf. A049054, A088274, A088275, A095688, A107083, A108049, A108050, A108052, A108054.

[n: n in [1..400]| IsPrime(10^n+99)]; // Vincenzo Librandi, Nov 02 2014

Select[Range[78000],PrimeQ[10^#+99]&] (* Harvey P. Dale, Aug 23 2013 *)

a(1)=1 added by Vladimir Joseph Stephan Orlovsky, May 02 2008
a(29)-a(33) from Robert Price, Mar 22 2010
a(34)=77726 from Robert Price, Mar 03 2011

A110918 Integers n such that 10^n+91 is a prime number.

Original entry on oeis.org

1, 2, 3, 4, 11, 12, 15, 19, 136, 144, 732, 5754, 6602, 23499, 39583, 74254, 93356, 94016

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Oct 04 2005

No additional terms < 100000.

See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "10091".

			n = 4 is a member: 10^4+91 = 10000+91 = 10091, which is prime.

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

Cf. A049054, A088274, A088275, A095688, A107083, A108049, A108050, A108052, A108054.

[n: n in [1..400]| IsPrime(10^n+91)]; // Vincenzo Librandi, Nov 02 2014

Select[Range[2000], PrimeQ[10^# + 91] &] (* Vincenzo Librandi, Nov 02 2014 *)

a(1)=1 added by Vladimir Joseph Stephan Orlovsky, May 02 2008
a(12)-a(15) from Robert Price, Dec 12 2010
Edited by Ray Chandler, Dec 23 2010
a(16)=74254 from Robert Price, Mar 03 2011
a(17)=92178 and a(18)=94016 from Robert Price, Apr 19 2011
a(17)=93356 corrected by Robert Price, Apr 19 2011
a(12) corrected by Tyler Busby, May 03 2024

A101392 Numbers k such that 2*10^k+9 is prime.

Original entry on oeis.org

0, 1, 5, 25, 455, 761, 9205, 13561, 15955, 26669, 113941

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Jan 15 2005

761 and 9205 only probably prime. No others less than 10000.

a(12) > 2*10^5. - Robert Price, Jun 06 2015

			n = 1, 5 are members since 29 and 200009 are primes.

Makoto Kamada, Prime numbers of the form 200...009.
Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers.

Cf. A081677, A088275, A101952.

Do[ If[ PrimeQ[2*10^n + 9], Print[n]], {n, 0, 10000}]

is(n)=ispseudoprime(2*10^n+9) \\ Charles R Greathouse IV, Jun 12 2017

a(n) = A101952(n-1) + 1 for n>1.

a(8)-a(9) from Kamada link by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
a(10)-a(11) from Kamada data by Robert Price, Dec 13 2010
Prepended a(1)=0 by Robert Price, Jun 06 2015

cp's OEIS Frontend

A108050 Integers k such that 10^k+21 is prime.

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A108049 Integers k such that 10^k + 43 is a prime number.

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A108052 Integers k such that 10^k+19 is a prime number.

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A108054 Integers k such that 10^k+49 is prime.

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A107083 Integers k such that 10^k + 31 is prime.

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A088274 Numbers k such that 10^k + 7 is prime.

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A108312 Integers n such that 10^n + 27 is prime.

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