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 A018239 Primorial primes: primes of the form 1 + product of first k primes, for some k. 25
 2, 3, 7, 31, 211, 2311, 200560490131, 1719620105458406433483340568317543019584575635895742560438771105058321655238562613083979651479555788009994557822024565226932906295208262756822275663694111 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Prime numbers that are the sum of two primorial numbers. - Juri-Stepan Gerasimov, Nov 08 2010 REFERENCES F. Iacobescu, Smarandache Partition Type and Other Sequences, Bull. Pure Appl. Sciences, Vol. 16E, No. 2 (1997), pp. 237-240. LINKS M. Fleuren, Factors and primes of Smarandache sequences. M. Fleuren, Smarandache Prime Product Sequence. R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670, 2012 - From N. J. A. Sloane, Jun 13 2012 F. Smarandache, Sequences of Numbers Involved in Unsolved Problems. R. Ondrejka, Primorial-Plus-One Primes FORMULA a(n) = 1 + A002110(A014545(n)), where A002110(k) is the product of the first k primes. - M. F. Hasler, Jun 23 2019 EXAMPLE From M. F. Hasler, Jun 23 2019: a(1) = 2 = 1 + product of the first 0 primes (i.e., the empty product = 1). a(2) = 3 = 1 + 2 = 1 + product of the first prime (= 2). a(3) = 7 = 1 + 2*3 = 1 + product of the first two primes. a(4) = 31 = 1 + 2*3*5 = 1 + product of the first three primes. a(5) = 211 = 1 + 2*3*5*7 = 1 + product of the first four primes. a(6) = 2311 = 1 + 2*3*5*7*11 = 1 + product of the first five primes. Then the product of the first 6, 7, ..., 9 or 10 primes does not yield a primorial prime, the next one is: a(7) = 200560490131 = 1 + 2*3*5*7*11*13*17*19*23*29*31 = 1 + product of the first eleven primes, and so on. See A014545 = (0, 1, 2, 3, 4, 5, 11, 75, 171, 172, ...) for the k's that yield a term. (End) MATHEMATICA Select[FoldList[Times, 1, Prime[Range]] + 1, PrimeQ]. (* Loreno Heer (helohe(AT)bluewin.ch), Jun 29 2004 *) PROG (PARI) P=1; print1(2); forprime(p=2, 1e6, if(isprime(1+P*=p), print1(", "P+1))) \\ Charles R Greathouse IV, Apr 28 2015 CROSSREFS Primes in A006862 (primorials plus 1). A005234 and A014545 (which are the main entries for this sequence) give more terms. Cf. A002110. Sequence in context: A241196 A073918 A096350 * A066279 A337221 A161471 Adjacent sequences:  A018236 A018237 A018238 * A018240 A018241 A018242 KEYWORD nonn,nice AUTHOR EXTENSIONS Edited by N. J. A. Sloane at the suggestion of Vladeta Jovovic, Jun 18 2007 Name edited by M. F. Hasler, Jun 23 2019 STATUS approved

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Last modified September 24 21:25 EDT 2020. Contains 337322 sequences. (Running on oeis4.)