A329727 Numbers k such that k^3 +- 2 and k +- 2 are prime.
129, 1491, 1875, 2709, 5655, 6969, 10335, 14325, 14421, 17319, 26559, 35109, 37509, 43719, 50229, 52629, 101871, 102795, 104325, 105501, 120429, 127599, 132699, 136395, 137829, 157521, 172425, 173685, 179481, 186189, 191829, 211371, 219681, 221199, 229215, 234195
Offset: 1
Keywords
Examples
a(1) = 129: 129^3 + 2 = 2146691; 129^3 - 2 = 2146687; 129 + 2 = 131; 129 - 2 = 127; all four results are prime. a(2) = 1491: 1491^3 + 2 = 3314613773; 1491^3 - 2 = 3314613769; 1491 + 2 = 1493; 1491 - 2 = 1489; all four results are prime.
Links
- Daniel Starodubtsev, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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Magma
[k:k in [1..250000]|forall{m:m in [-2,2]|IsPrime(k+m) and IsPrime(k^3+m)}]; // Marius A. Burtea, Nov 20 2019 -
Mathematica
Select[Range[500000], PrimeQ[#^3 + 2] && PrimeQ[#^3 - 2] && PrimeQ[# + 2] && PrimeQ[# - 2] &]
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PARI
isok(k) = isprime(k-2) && isprime(k+2) && isprime(k^3-2) && isprime(k^3+2); \\ Michel Marcus, Nov 24 2019
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PARI
list(lim)=my(v=List(),p=127,k); forprime(q=131,lim+2,if(q-p==4 && isprime((k=p+2)^3-2) && isprime(k^3+2), listput(v,k)); p=q); Vec(v) \\ Charles R Greathouse IV, May 06 2020
Comments