A088274 -id:A088274 - 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

A088275 Numbers k such that 10^k + 9 is prime.

Original entry on oeis.org

1, 2, 3, 4, 9, 18, 22, 45, 49, 56, 69, 146, 202, 272, 2730, 2841, 4562, 31810, 43186, 48109, 92691, 237670, 400310, 482706

Offset: 1

Amarnath Murthy, Sep 28 2003

No others less than 9000. - Julien Peter Benney (jpbenney(AT)ftml.net), Jan 15 2005
No others less than 39254. - Dirk Augustin, Oct 24 2006
2730, 2841 and 4562 all give primes. - Joao da Silva (zxawyh66(AT)yahoo.com), Sep 30 2005
Verified existing terms. No other terms less than 40001. - Robert Price, Aug 14 2010
No other terms <= 100000. - Robert Price, Mar 03 2011
a(23) > 3*10^5. - Robert Price, Oct 26 2023

			4 is a member since 10^4 + 9 = 10009 is a prime.

Henri Lifchitz and Renaud Lifchitz (Editors), Search for 10^k+9, PRP Top Records.
Makoto Kamada, Prime numbers of the form 100...009.
Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers, Smarandache Notions Journal, 2003.

Cf. A049054, A088274, A102008.

Do[ If[ PrimeQ[ 10^n + 9], Print[n]], {n, 0, 10000}] (* Robert G. Wilson v, Dec 16 2004 *)

is(n)=isprime(10^n + 9) \\ Charles R Greathouse IV, Apr 29 2015

a(n) = A102008(n) + 1.

a(8)-a(16) from Ray Chandler, Oct 10 2003
a(17) from Julien Peter Benney (jpbenney(AT)ftml.net), Jan 15 2005
a(18) (a PRP) found by Dirk Augustin, Oct 16 2006
a(19)-a(20) (probable primes), found with WinPFGW. No others less than 60400. - Jason Earls, Dec 22 2007
a(21) from Robert Price, Mar 03 2011
a(22) from Robert Price, Oct 26 2023
a(23) from Boyan Hu, Jun 15 2025
a(24) from Boyan Hu, Jun 24 2025

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

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

A159031 Primes of the form "1 [0]_n 7" - with zeros between 1 and 7.

Original entry on oeis.org

17, 107, 10007, 100000007, 1000000007, 1000000000000000000000007, 1000000000000000000000000000000000000000000000000000000000007

Offset: 1

Parthasarathy Nambi, Apr 02 2009

The next term, a(8), has 111 digits. - Harvey P. Dale, Nov 12 2011

			1000000000000000000000007 is a prime with 23 zeros between 1 and 7.

Dario Alejandro Alpern, Factorization using the Elliptic Curve Method.
Makoto Kamada, Prime numbers of the form 100...007.
Index entries for primes involving repunits.

Cf. A088274. - Robert G. Wilson v, Apr 05 2009

Do[ If[ PrimeQ[10^n + 7], Print[10^n + 7]], {n, 100}] (* Robert G. Wilson v, Apr 05 2009 *)
Select[Table[FromDigits[Join[{1},PadRight[{},n,0],{7}]],{n,0,120}],PrimeQ] (* Harvey P. Dale, Nov 12 2011 *)

a(7) from Robert G. Wilson v, Apr 05 2009

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

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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A088275 Numbers k such that 10^k + 9 is prime.

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

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

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