cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A096177 Primes p such that primorial(p)/2 + 2 is prime.

Original entry on oeis.org

2, 3, 5, 7, 13, 29, 31, 37, 47, 59, 109, 223, 307, 389, 457, 1117, 1151, 2273, 9137, 10753, 15727, 25219, 26459, 29251, 30259, 52901, 194471
Offset: 1

Views

Author

Hugo Pfoertner, Jun 27 2004

Keywords

Comments

a(27) > 172000. - Robert Price, May 10 2019
Some of the results were computed using the PrimeFormGW (PFGW) primality-testing program. - Hugo Pfoertner, Nov 16 2019

Examples

			a(3)=7 because primorial(7)/2 + 2 = A070826(4) + 2 = 2*3*5*7/2 + 2 = 107 is prime.

Crossrefs

Cf. A070826, A096178 primes of the form primorial(p)/2+2, A096547 primes p such that primorial(p)/2-2 is prime, A067024 smallest p+2 that has n distinct prime factors, A014545 primorial primes, A087398.

Programs

  • Mathematica
    k = 1; Do[If[PrimeQ[n], k = k*n; If[PrimeQ[k/2 + 2], Print[n]]], {n, 2, 100000}] (* Ryan Propper, Jul 03 2005 *)
  • PARI
    P=1/2;forprime(p=2,1e4,if(isprime((P*=p)+2), print1(p", "))) \\ Charles R Greathouse IV, Mar 14 2011

Extensions

7 additional terms, corresponding to probable primes, from Ryan Propper, Jul 03 2005
Edited by T. D. Noe, Oct 30 2008
a(26) from Robert Price, May 10 2019
a(27) from Tyler Busby, Mar 17 2024

A087398 Primes of the form primorial(P(k))/2-2.

Original entry on oeis.org

13, 103, 1153, 15013, 255253, 4849843, 111546433, 100280245063, 152125131763603, 16294579238595022363, 278970415063349480483707693, 11992411764462614086353260819346129198103, 481473710367991963528473107950567214598209565303106537707981745633
Offset: 1

Views

Author

Cino Hilliard, Oct 21 2003

Keywords

Comments

Twinmorial numbers are the partial products of twin primes. Sum of reciprocals = 0.08756985926348207565388288916..
The next term (a(14)) has 174 digits. - Harvey P. Dale, Mar 30 2013

Links

Crossrefs

Cf. A096177 primes k such that primorial(k)/2+2 is prime, A096178 primes of the form primorial(k)/2+2, A096547 Primes k such that primorial(k)/2-2 is prime, A067024 smallest p+2 that has n distinct prime factors, A014545 primorial primes.

Programs

  • Mathematica
    Select[#/2-2&/@Rest[FoldList[Times,1,Prime[Range[100]]]],PrimeQ] (* Harvey P. Dale, Mar 30 2013 *)
  • PARI
    twimorial(n) = { s=0; p=3; forprime(x=5,n, if(isprime(x-2),c1++); p=p*x; if(isprime(p-2), print1(p-2","); c2++; s+=1.0/(p-2); ) ); print(); print(s) }
  • PARI
    v=[];pr=1; forprime(p=3,2357,pr*=p; if(ispseudoprime(pr-2),v=concat(v,pr-2))) \\ Charles R Greathouse IV, Feb 14 2011

Formula

Twins 3*5 = 15 = p+2. p=13.

Extensions

Description corrected by Hugo Pfoertner, Jun 25 2004
One more term (a(13)) added by Harvey P. Dale, Mar 30 2013

A096178 Primes of the form primorial(p)/2+2.

Original entry on oeis.org

3, 5, 17, 107, 15017, 3234846617, 100280245067, 3710369067407, 307444891294245707, 961380175077106319537, 139867498408927468089138080936033904837498617
Offset: 1

Views

Author

Hugo Pfoertner, Jun 27 2004

Keywords

Comments

Primes of the form A070826(n)+2.

Examples

			a(4) = 107 because 107 is a prime of the form primorial(7)/2 + 2 = A070826(4) + 2 = 2*3*5*7/2 + 2.

Links

Crossrefs

Cf. A070826, A096177 (primorial(p)/2+2 is prime), A096547 (primorial(p)/2-2 is prime), A067024 (smallest p+2 that has n distinct prime factors), A014545 (primorial primes), A087398.

Programs

  • PARI
    for(n=1,30,p=prod(k=1,n,prime(k))/2+2;if(ispseudoprime(p),print1(p,", "))) \\ Hugo Pfoertner, Dec 26 2019

Formula

a(n) = A070826(A096177(n)) + 2. - Amiram Eldar, Dec 26 2019

Extensions

a(1) inserted by Amiram Eldar, Dec 26 2019

A178642 Primes p such that primorial(p)/2 - 2 is not prime.

Original entry on oeis.org

3, 29, 37, 43, 47, 59, 61, 67, 73, 79, 83, 89, 97, 101, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, May 31 2010

Keywords

Examples

			3*5*7*11*13*17*19*23*29 - 2 = 43*167*450473 is composite.

Crossrefs

Cf. A002110, A096177, A096547, A178641.

Programs

  • Mathematica
    pp=1;lst={};Do[p=Prime[n];pp*=p;If[ !PrimeQ[pp-2],AppendTo[lst,p]],{n,2,2*5!}];lst
Transpose[Select[With[{pros=Rest[FoldList[Times,1,Prime[Range[100]]]]}, Table[ {Prime[n], pros[[n]]},{n,100}]],!PrimeQ[Last[#]/2-2]&]][[1]] (* Harvey P. Dale, Mar 02 2012 *)

A178648 Primes p such that primorial(p)/2 +- 2 are primes.

Original entry on oeis.org

5, 7, 13, 31
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, May 31 2010

Keywords

Comments

No further terms up to the 500th prime, i.e., 3571. - Harvey P. Dale, May 09 2023

Examples

			3*5 = 15; 15-2 and 15+2 are primes.

Links

Crossrefs

Cf. A070826, A178641, A178642.
Intersection of A096177 and A096547.

Programs

  • Mathematica
    pp=1;lst={};Do[p=Prime[n];pp*=p;If[PrimeQ[pp-2]&&PrimeQ[pp+2],Print[Date[],p];AppendTo[lst,p]],{n,2,4!}];lst
Module[{nn=15,pr,pm},pr=Prime[Range[nn]];pm=FoldList[Times,pr];Select[Thread[ {pr,pm}],AllTrue[ #[[2]]/2+{2,-2},PrimeQ]&]][[;;,1]] (* Harvey P. Dale, May 09 2023 *)
Showing 1-5 of 5 results.

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