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- Factorial_prime abstract "A factorial prime is a prime number that is one less or one more than a factorial (all factorials > 1 are even). The first few factorial primes are:2 (0! + 1 or 1! + 1), 3 (2! + 1), 5 (3! − 1), 7 (3! + 1), 23 (4! − 1), 719 (6! − 1), 5039 (7! − 1), 39916801 (11! + 1), 479001599 (12! − 1), 87178291199 (14! − 1), ... (sequence A088054 in OEIS)n! − 1 is prime for (sequence A002982 in OEIS):n = 3, 4, 6, 7, 12, 14, 30, 32, 33, 38, 94, 166, 324, 379, 469, 546, 974, 1963, 3507, 3610, 6917, 21480, 34790, 94550, 103040, 147855, ...n! + 1 is prime for (sequence A002981 in OEIS):n = 0, 1, 2, 3, 11, 27, 37, 41, 73, 77, 116, 154, 320, 340, 399, 427, 872, 1477, 6380, 26951, 110059, 150209, ... No other factorial primes are known as of September 2013.Absence of primes to both sides of a factorial n! implies a relatively lengthy run of consecutive composite numbers, since n! ± k is divisible by k for 2 ≤ k ≤ n. For example, the next prime following 6227020777 = 13! − 23 is 6227020867 = 13! + 67 (a run of 89 consecutive composites); here the run is substantially longer than implied merely by the absence of factorial primes. Note that this is not the most efficient way to find large prime gaps. E.g., there are 95 consecutive composites between the primes 360653 and 360749.".
- Factorial_prime wikiPageExternalLink page.php?id=30.
- Factorial_prime wikiPageExternalLink 30721.
- Factorial_prime wikiPageID "409293".
- Factorial_prime wikiPageRevisionID "571692466".
- Factorial_prime hasPhotoCollection Factorial_prime.
- Factorial_prime title "Factorial Prime".
- Factorial_prime urlname "FactorialPrime".
- Factorial_prime subject Category:Classes_of_prime_numbers.
- Factorial_prime subject Category:Factorial_and_binomial_topics.
- Factorial_prime subject Category:Integer_sequences.
- Factorial_prime type Abstraction100002137.
- Factorial_prime type Arrangement107938773.
- Factorial_prime type Class107997703.
- Factorial_prime type ClassesOfPrimeNumbers.
- Factorial_prime type Collection107951464.
- Factorial_prime type Group100031264.
- Factorial_prime type IntegerSequences.
- Factorial_prime type Ordering108456993.
- Factorial_prime type Sequence108459252.
- Factorial_prime type Series108457976.
- Factorial_prime comment "A factorial prime is a prime number that is one less or one more than a factorial (all factorials > 1 are even). The first few factorial primes are:2 (0! + 1 or 1! + 1), 3 (2! + 1), 5 (3! − 1), 7 (3! + 1), 23 (4! − 1), 719 (6! − 1), 5039 (7! − 1), 39916801 (11! + 1), 479001599 (12! − 1), 87178291199 (14! − 1), ...".
- Factorial_prime label "Factorial prime".
- Factorial_prime label "Fakultätsprimzahl".
- Factorial_prime label "Nombre premier factoriel".
- Factorial_prime label "Primo fattoriale".
- Factorial_prime label "Факториальное простое число".
- Factorial_prime label "阶乘素数".
- Factorial_prime label "階乗素数".
- Factorial_prime sameAs Fakultätsprimzahl.
- Factorial_prime sameAs Nombre_premier_factoriel.
- Factorial_prime sameAs Primo_fattoriale.
- Factorial_prime sameAs 階乗素数.
- Factorial_prime sameAs m.024vxb.
- Factorial_prime sameAs Q973861.
- Factorial_prime sameAs Q973861.
- Factorial_prime sameAs Factorial_prime.
- Factorial_prime wasDerivedFrom Factorial_prime?oldid=571692466.
- Factorial_prime isPrimaryTopicOf Factorial_prime.