A154114 -id:A154114 - 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

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

A176115 Numbers n such that 2310n-1, 2310n+1 are twin primes, (2310=235711).

Original entry on oeis.org

1, 4, 5, 11, 15, 19, 24, 34, 40, 48, 51, 58, 66, 73, 78, 97, 98, 100, 106, 109, 116, 117, 123, 129, 130, 134, 136, 137, 143, 163, 169, 175, 176, 180, 182, 186, 194, 201, 207, 222, 226, 228, 234, 239, 248, 271, 274, 275, 279, 285, 286, 295, 305, 313, 320, 347

Offset: 1

Vladimir Joseph Stephan Orlovsky, Apr 08 2010

nonn

Cf. A002822, A075749, A154114, A176114

Select[Range[6! ],PrimeQ[2310*#-1]&&PrimeQ[2310*#+1]&]

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

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

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

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

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A176115 Numbers n such that 2310*n-1, 2310*n+1 are twin primes, (2310=2*3*5*7*11).

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A176115 Numbers n such that 2310n-1, 2310n+1 are twin primes, (2310=235711).