A045320 -id:A045320 - cp's OEIS frontend

A049481 Primes p such that p + 30 is also prime.

7, 11, 13, 17, 23, 29, 31, 37, 41, 43, 53, 59, 67, 71, 73, 79, 83, 97, 101, 107, 109, 127, 137, 149, 151, 163, 167, 181, 193, 197, 199, 211, 227, 233, 239, 241, 251, 263, 277, 281, 283, 307, 317, 337, 349, 353, 359, 367, 379, 389, 401, 409, 419, 431, 433, 449

Offset: 1

Labos Elemer

nonn

30 = A002110(3) is the 3rd primorial number.

p and p+30 are not necessarily consecutive primes. Initial segment of A045320 is identical, but 113 is not in this sequence because 113 + 30 = 143 is divisible by 13.

			7 is a term since it is prime and 7 + 30 = 37 is also prime.

Harvey P. Dale, Table of n, a(n) for n = 1..10000
Hugo Pfoertner, Observed ratio n*log(a(n))/pi(a(n)) for n=10^7..5.6*10^9 with a conjectured extrapolation for large n (2024).

Cf. A002110, A045320, A005597.

Cf. A001359, A023201, A049482, A049483, A049484, A049485, A154114.

lst={};Do[p=Prime[n];If[PrimeQ[p+30],AppendTo[lst,p]],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 04 2009 *)
Select[Prime[Range[100]],PrimeQ[#+30]&] (* Harvey P. Dale, Apr 28 2012 *)

isok(p) = isprime(p) && isprime(p + 30); \\ Amiram Eldar, Mar 15 2025

Assuming Polignac's conjecture and the first Hardy-Littlewood conjecture: Limit_{n->oo} n*log(a(n))/primepi(a(n)) = (16/3)*A005597 = 3.52086... . - Alain Rocchelli, Oct 29 2024

A045458 Primes congruent to 5 mod 7.

Original entry on oeis.org

5, 19, 47, 61, 89, 103, 131, 173, 229, 257, 271, 313, 383, 397, 439, 467, 509, 523, 593, 607, 677, 691, 719, 733, 761, 859, 887, 929, 971, 1013, 1069, 1097, 1153, 1181, 1223, 1237, 1279, 1307, 1321, 1433, 1447, 1489, 1531, 1559, 1601, 1657, 1699, 1741, 1783

Offset: 1

N. J. A. Sloane

Subsequence of A017041. - Michel Marcus, May 06 2014

Primes congruent to 5 mod 14. - Chai Wah Wu, Apr 28 2025

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A045320 (complement), A017041, A045471, A045473.

[ p: p in PrimesUpTo(11000) | p mod 7 eq 5 ]; // Vincenzo Librandi, Aug 13 2012

Select[Range[5, 50000, 7], PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Jun 13 2011 *)

is(n)=isprime(n) && n%7==5 \\ Charles R Greathouse IV, Jul 01 2016

A045334 Primes congruent to {1, 2, 3, 4, 6} (mod 7).

Original entry on oeis.org

2, 3, 11, 13, 17, 23, 29, 31, 37, 41, 43, 53, 59, 67, 71, 73, 79, 83, 97, 101, 107, 109, 113, 127, 137, 139, 149, 151, 157, 163, 167, 179, 181, 191, 193, 197, 199, 211, 223, 227, 233, 239, 241, 251, 263, 269, 277

Offset: 1

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A045320.

[p: p in PrimesUpTo(500) | p mod 7 in [1, 2, 3, 4, 6]]; // Vincenzo Librandi, Aug 08 2012

Select[Prime[Range[400]],MemberQ[{1,2,3,4,6},Mod[#,7]]&] (* Vincenzo Librandi, Aug 08 2012 *)

A049482 Primes p such that p + 210 is also prime.

Original entry on oeis.org

13, 17, 19, 23, 29, 31, 41, 47, 53, 59, 61, 67, 71, 73, 83, 97, 101, 103, 107, 127, 137, 139, 149, 157, 163, 173, 179, 191, 199, 211, 223, 229, 233, 239, 251, 257, 269, 277, 281, 293, 311, 313, 331, 337, 347, 353, 359, 367, 383, 389, 397, 409, 421, 431, 433

Offset: 1

Labos Elemer

nonn

			Both 13 and 13 + 210 = 223 are prime.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A045320, A001359, A023201, A049481.

Select[Prime@ Range@ 84, PrimeQ[# + 210] &] (* Michael De Vlieger, Jun 29 2017 *)

list(lim)=my(v=List()); forprime(p=2,lim, if(isprime(p+210), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Feb 23 2017

a(n) >> n log^2 n. - Charles R Greathouse IV, Feb 23 2017

A049485 Primes p such that p + 510510 is also prime, where 510510 is the 7th primorial number A002110(7).

Original entry on oeis.org

19, 41, 43, 59, 71, 73, 79, 101, 103, 107, 109, 167, 173, 181, 197, 199, 241, 257, 263, 283, 293, 307, 313, 317, 337, 379, 397, 409, 421, 431, 433, 479, 491, 503, 509, 523, 547, 577, 599, 601, 613, 641, 643, 653, 659, 661, 683, 691, 701, 727, 733, 751, 769

Offset: 1

Labos Elemer

nonn

p and p+510510 are not necessarily consecutive primes.

			19 is a term since it is prime and 19 + 510510 = 510529 is also prime.

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A002110, A045320.

Cf. A001359, A023201, A049481, A049482, A049483, A049484, A154114.

lst={};Do[p=Prime[n];If[PrimeQ[p+510510],AppendTo[lst,p]],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 04 2009 *)

isok(p) = isprime(p) && isprime(p + 510510); \\ Amiram Eldar, Mar 15 2025

A049483 Primes p such that p + 2310 is also prime, where 2310 is the 5th primorial number A002110(5).

Original entry on oeis.org

23, 29, 31, 37, 41, 47, 61, 67, 71, 73, 79, 83, 89, 101, 107, 113, 127, 131, 137, 149, 157, 163, 167, 193, 211, 229, 233, 239, 241, 269, 281, 283, 307, 311, 337, 347, 349, 353, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 439, 443, 457, 467, 479

Offset: 1

Labos Elemer

nonn

p and p+2310 are not necessarily consecutive primes.

			23 is a term since it is prime and 23 + 2310 = 2333 is also prime.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Cf. A002110, A045320.

Cf. A001359, A023201, A049481, A049482, A049484, A049485, A154114.

Select[Prime[Range[100]],PrimeQ[#+2310]&] (* Harvey P. Dale, Nov 15 2012 *)

isok(p) = isprime(p) && isprime(p + 2310); \\ Amiram Eldar, Mar 15 2025

A049484 Primes p such that p + 30030 is also prime, where 30030 is the 6th primorial number A002110(6).

Original entry on oeis.org

17, 29, 41, 59, 61, 67, 73, 79, 83, 89, 103, 107, 109, 131, 139, 151, 157, 167, 173, 181, 193, 211, 223, 229, 239, 241, 263, 277, 283, 293, 311, 317, 337, 359, 373, 397, 401, 419, 439, 461, 463, 467, 479, 487, 499, 509, 523, 547, 563, 601, 607, 613, 619, 631

Offset: 1

Labos Elemer

nonn

p and p+30030 are not necessarily consecutive primes.

			17 is a term since it is prime and 17 + 30030 = 30047 is also prime.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A002110, A045320.

Cf. A001359, A023201, A049481, A049482, A049483, A049485, A154114.

Select[Prime[Range[150]],PrimeQ[#+30030]&] (* Harvey P. Dale, Sep 21 2022 *)

isok(p) = isprime(p) && isprime(p + 30030); \\ Amiram Eldar, Mar 15 2025

A215322 Primes congruent to {1, 2, 3, 4, 6} mod 11.

Original entry on oeis.org

2, 3, 13, 17, 23, 37, 47, 59, 61, 67, 79, 83, 89, 101, 103, 113, 127, 149, 157, 167, 179, 191, 193, 199, 211, 223, 233, 257, 277, 281, 311, 331, 347, 353, 367, 389, 397, 409, 419, 421, 431, 433, 443, 457, 463, 479, 487, 499, 509, 521, 523, 541, 563, 587

Offset: 1

Vincenzo Librandi, Aug 08 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A045320, A045334.

[p: p in PrimesUpTo(600) | p mod 11 in [1, 2, 3, 4, 6]];

Select[Prime[Range[400]],MemberQ[{1,2,3,4,6},Mod[#,11]]&]

A215323 Primes congruent to {1, 2, 3, 4, 6} mod 13.

Original entry on oeis.org

2, 3, 17, 19, 29, 41, 43, 53, 67, 71, 79, 97, 107, 131, 149, 157, 173, 197, 199, 211, 223, 227, 251, 263, 277, 313, 331, 353, 367, 379, 383, 409, 419, 431, 433, 443, 457, 461, 487, 509, 521, 523, 547, 563, 587, 599, 601, 613, 617, 641, 643, 653, 677, 691

Offset: 1

Vincenzo Librandi, Aug 08 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A045320, A045334.

[p: p in PrimesUpTo(800) | p mod 13 in [1, 2, 3, 4, 6]];

Select[Prime[Range[400]],MemberQ[{1,2,3,4,6},Mod[#,13]]&]

A215324 Primes congruent to {1, 2, 3, 4, 6} mod 17.

Original entry on oeis.org

2, 3, 19, 23, 37, 53, 71, 89, 103, 137, 139, 157, 173, 191, 193, 223, 227, 239, 241, 257, 293, 307, 359, 397, 409, 431, 443, 461, 463, 479, 499, 547, 563, 599, 601, 613, 631, 647, 683, 701, 733, 751, 769, 839, 853, 887, 907, 919, 937, 941, 953, 971

Offset: 1

Vincenzo Librandi, Aug 08 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A045320, A045334.

[p: p in PrimesUpTo(1000) | p mod 17 in [1, 2, 3, 4, 6]];

Select[Prime[Range[400]],MemberQ[{1,2,3,4,6},Mod[#,17]]&]

cp's OEIS Frontend

A049481 Primes p such that p + 30 is also prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A045458 Primes congruent to 5 mod 7.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

A045334 Primes congruent to {1, 2, 3, 4, 6} (mod 7).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

A049482 Primes p such that p + 210 is also prime.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A049485 Primes p such that p + 510510 is also prime, where 510510 is the 7th primorial number A002110(7).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

A049483 Primes p such that p + 2310 is also prime, where 2310 is the 5th primorial number A002110(5).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

A049484 Primes p such that p + 30030 is also prime, where 30030 is the 6th primorial number A002110(6).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

A215322 Primes congruent to {1, 2, 3, 4, 6} mod 11.

Views

Author