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A226461
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Numbers n such that the following are six primes: 2*n^2 +- 1, 3*n^2 +- 1, 5*n^2 +- 1.
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1
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6, 2100, 20586, 669054, 745590, 6556122, 9317496, 10190796, 15648732, 18215196, 25561410, 35613990, 36710652, 38649066, 41124594, 41711874, 46576524, 48701400, 49406358, 59278296, 70038948, 74993808, 75553092, 83606418, 84182154, 88000374, 92527764, 98969052, 100691976
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OFFSET
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1,1
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COMMENTS
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6 is in the sequence because the following are six primes: 71, 73, 107, 109, 179, 181.
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LINKS
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MATHEMATICA
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spQ[n_]:=AllTrue[Flatten[{2n^2+{1, -1}, 3n^2+{1, -1}, 5n^2+{1, -1}}], PrimeQ]; Select[ Range[101*10^6], spQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 28 2015 *)
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PROG
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(Java)
import java.math.BigInteger;
public static void main (String[] args) {
for (long n = 1; n < (1L << 30); n++)
long x = n*n*5;
BigInteger b = BigInteger.valueOf(x+1);
if (!b.isProbablePrime(80)) continue;
b = BigInteger.valueOf(x-1);
if (!b.isProbablePrime(80)) continue;
x = n*n*2;
b = BigInteger.valueOf(x+1);
if (!b.isProbablePrime(80)) continue;
b = BigInteger.valueOf(x-1);
if (!b.isProbablePrime(80)) continue;
x = n*n*3;
b = BigInteger.valueOf(x+1);
if (!b.isProbablePrime(80)) continue;
b = BigInteger.valueOf(x-1);
if (!b.isProbablePrime(80)) continue;
System.out.printf("%d, ", n);
}
}
}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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