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
a(3)=7 because primorial(7)/2 + 2 = A070826(4) + 2 = 2*3*5*7/2 + 2 = 107 is prime.
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k = 1; Do[If[PrimeQ[n], k = k*n; If[PrimeQ[k/2 + 2], Print[n]]], {n, 2, 100000}] (* Ryan Propper, Jul 03 2005 *)
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P=1/2;forprime(p=2,1e4,if(isprime((P*=p)+2), print1(p", "))) \\ Charles R Greathouse IV, Mar 14 2011
7 additional terms, corresponding to probable primes, from
Ryan Propper, Jul 03 2005
A096547
Primes p such that primorial(p)/2 - 2 is prime.
Original entry on oeis.org
5, 7, 11, 13, 17, 19, 23, 31, 41, 53, 71, 103, 167, 431, 563, 673, 727, 829, 1801, 2699, 4481, 6121, 7283, 9413, 10321, 12491, 17807, 30307, 31891, 71917, 172517
Offset: 1
Prime 7 is a term because primorial(7)/2 - 2 = A034386(7)/2 - 2 = 2*3*5*7/2 - 2 = 103 is prime.
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b:= proc(n) b(n):= `if`(n=0, 1, `if`(isprime(n), n, 1)*b(n-1)) end:
q:= p-> isprime(p) and isprime(b(p)/2-2):
select(q, [$1..500])[];
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k = 1; Do[k *= Prime[n]; If[PrimeQ[k - 2], Print[Prime[n]]], {n, 2, 3276}] (* Ryan Propper, Oct 25 2005 *)
Prime[#]&/@Flatten[Position[FoldList[Times,Prime[Range[1000]]]/2-2,?PrimeQ]] (* _Harvey P. Dale, Jun 09 2023 *)
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
a(4) = 107 because 107 is a prime of the form primorial(7)/2 + 2 = A070826(4) + 2 = 2*3*5*7/2 + 2.
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for(n=1,30,p=prod(k=1,n,prime(k))/2+2;if(ispseudoprime(p),print1(p,", "))) \\ Hugo Pfoertner, Dec 26 2019
Showing 1-3 of 3 results.
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