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 A053182 Primes p such that p^2 + p + 1 is prime. 36
 2, 3, 5, 17, 41, 59, 71, 89, 101, 131, 167, 173, 293, 383, 677, 701, 743, 761, 773, 827, 839, 857, 911, 1091, 1097, 1163, 1181, 1193, 1217, 1373, 1427, 1487, 1559, 1583, 1709, 1811, 1847, 1931, 1973, 2129, 2273, 2309, 2339, 2411, 2663, 2729, 2789, 2957 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Roger Horn computed the first 776 terms of this sequence around 1961 to test (with Paul Bateman) their conjecture on the density of simultaneous primes in polynomials. - Charles R Greathouse IV, Apr 05 2011 Starting with a(3)=5 all terms are of the form 6k-1, k in A147683. - Zak Seidov, Nov 10 2008 Primes p such that the sum of divisors of p^2 (sigma(p^2) = A000203(p^2) = p^2+p+1) is prime. - Claudio Meller, Apr 07 2011 The generated prime numbers p^2 + p + 1 are exactly A053183. - Bernard Schott, Dec 20 2012 Positive squarefree k such that the sum of divisors of k^2 is prime. - Peter Munn, Feb 02 2018 LINKS M. F. Hasler, Table of n, a(n) for n = 1..2650 (Terms up to 500000) Paul T. Bateman and Roger A. Horn, A heuristic asymptotic formula concerning the distribution of prime numbers, Math. Comp. 16 (1962), 363-367. Paolo Santonastaso and Ferdinando Zullo, Linearized trinomials with maximum kernel, arXiv:2012.14861 [math.NT], 2020. MATHEMATICA Select[Prime[Range], PrimeQ[#^2+#+1]&] (* Bruno Berselli, Nov 08 2011 *) PROG (PARI) isA053182(n)=isprime(n) && isprime(n^2+n+1)  \\ Michael B. Porter, Apr 23 2010 (PARI) c=0; forprime(p=1, default(primelimit), isprime(p^2+p+1) & write("/tmp/b053182.txt", c++, " "p))  \\ M. F. Hasler, Apr 07 2011 (MAGMA) [p: p in PrimesUpTo(10000) | IsPrime(p^2+p+1)]; // Vincenzo Librandi, Aug 06 2010 CROSSREFS Cf. A053184, A065508, A091567, A147683, A188596. Sequence in context: A189536 A163588 A270539 * A211972 A339855 A076706 Adjacent sequences:  A053179 A053180 A053181 * A053183 A053184 A053185 KEYWORD easy,nonn,changed AUTHOR Enoch Haga, Mar 01 2000 EXTENSIONS List changed to cross-reference by Franklin T. Adams-Watters, May 12 2010 STATUS approved

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Last modified April 17 06:46 EDT 2021. Contains 343059 sequences. (Running on oeis4.)