A063499
Primes of the form prime(n) + n!.
Original entry on oeis.org
3, 5, 11, 31, 131, 733, 362903, 39916831, 355687428096059, 6402373705728061, 15511210043330985984000097, 8222838654177922817725562880000127, 815915283247897734345611269596115894272000000173
Offset: 1
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[a: n in [1..50] | IsPrime(a) where a is NthPrime(n) + Factorial(n) ]; // Vincenzo Librandi, Apr 05 2015
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Select[Table[Prime[n] + n!, {n, 1, 60}], PrimeQ] (* Vincenzo Librandi, Apr 05 2015 *)
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for(n=1,70,x=prime(n)+n!; if(isprime(x),print(x)))
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{ n=0; f=1; for (m=1, 10^9, f*=m; if (isprime(a=prime(m) + f), write("b063499.txt", n++, " ", a); if (n==18, break)) ) } \\ Harry J. Smith, Aug 24 2009
A143933
a(n) is the smallest prime x such that x^2-n! is also prime.
Original entry on oeis.org
2, 2, 3, 11, 19, 31, 79, 211, 607, 1931, 6337, 21961, 78919, 295291, 1143563, 4574149, 18859777, 80014843, 348776611, 1559776279, 7147792903, 33526120129, 160785623729, 787685471519, 3938427356629, 20082117944579, 104349745809137, 552166953567737
Offset: 1
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f:= proc(n) local p,t;
t:= n!;
p:= floor(sqrt(t));
do
p:= nextprime(p);
if isprime(p^2-t) then return p fi
od
end proc:
map(f, [$1..28]); # Robert Israel, Feb 10 2019
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f[n_] := Block[{p = NextPrime[ Sqrt[ n!]]}, While[ !PrimeQ[p^2 - n!], p = NextPrime@ p]; p]; Array[f, 27] (* Robert G. Wilson v, Jan 08 2015 *)
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a(n)=my(N=n!,x=sqrtint(N)+1); while(!isprime(x^2-N), x=nextprime(x+1)); x \\ Charles R Greathouse IV, Dec 09 2014
A143931
a(n) is the smallest positive integer x such that x^2 - n! is prime.
Original entry on oeis.org
2, 2, 3, 11, 19, 31, 79, 209, 607, 1921, 6337, 21907, 78913, 295289, 1143539, 4574149, 18859733, 80014841, 348776611, 1559776279, 7147792823, 33526120127, 160785623627, 787685471389, 3938427356623, 20082117944263, 104349745809077
Offset: 1
a(1)=2 because 2^2-1! = 3 is prime;
a(2)=2 because 2^2-2! = 2 is prime;
a(3)=3 because 3^2-3! = 3 is prime;
a(4)=11 because 11^2-4! = 97 is prime.
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a = {}; Do[k = Round[Sqrt[n! ]] + 1; While[ ! PrimeQ[k^2 - n! ], k++ ]; AppendTo[a, k], {n, 1, 50}]; a
spi[n_]:=Module[{k=Ceiling[Sqrt[n!]],nf=n!},While[!PrimeQ[k^2-nf],k++];k]; Array[ spi,30] (* Harvey P. Dale, Feb 17 2023 *)
A143932
a(n) = smallest positive prime number of the form x^2 - n! (where x is a positive integer).
Original entry on oeis.org
3, 2, 3, 97, 241, 241, 1201, 3361, 5569, 61441, 240769, 915049, 240769, 17302321, 7076521, 49186201, 2100735289, 1074527281, 23971813321, 32354445841, 68820869329, 2992426816129, 26238323995129, 104071698229321
Offset: 1
a(1)=3 because 2^2 - 1! = 3;
a(2)=2 because 2^2 - 2! = 2;
a(3)=3 because 3^2 - 3! = 3;
a(4)=97 because 11^2 - 4! = 97.
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b = {}; Do[k = Round[Sqrt[n! ]] + 1; While[ ! PrimeQ[k^2 - n! ], k++ ]; AppendTo[b, k^2-n! ], {n, 1, 50}]; b
A261809
a(n) = n! - prime(n).
Original entry on oeis.org
-1, -1, 1, 17, 109, 707, 5023, 40301, 362857, 3628771, 39916769, 479001563, 6227020759, 87178291157, 1307674367953, 20922789887947, 355687428095941, 6402373705727939, 121645100408831933, 2432902008176639929, 51090942171709439927, 1124000727777607679921
Offset: 1
For n=4, a(4) = 4! - prime(4) = 24 - 7 = 17.
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[Factorial(n)-NthPrime(n): n in [1..30]]; // Vincenzo Librandi, Sep 02 2015
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Table[n! - Prime[n], {n,1,150}] (* G. C. Greubel, Sep 01 2015 *)
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vector(50, n, n!-prime(n))
A104079
Numbers of the form prime(n) + n! such that Gamma(n) + prime(n) is prime.
Original entry on oeis.org
3, 11, 31, 40339, 362903, 479001637, 8683317618811886495518194401280000137, 295232799039604140847618609643520000139
Offset: 1
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a = Delete[Union[Table[If[PrimeQ[ Gamma[n] + Prime[n]] == True, n! + Prime[n], 0], {n, 1, 100}]], 1]
Showing 1-6 of 6 results.
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