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- Fortunate_number abstract "A Fortunate number, named after Reo Fortune, for a given positive integer n is the smallest integer m > 1 such that pn# + m is a prime number, where the primorial pn# is the product of the first n prime numbers.For example, to find the seventh Fortunate number, one would first calculate the product of the first seven primes (2, 3, 5, 7, 11, 13 and 17), which is 510510. Adding 2 to that gives another even number, while adding 3 would give another multiple of 3. One would similarly rule out the integers up to 18. Adding 19, however, gives 510529, which is prime. Hence 19 is a Fortunate number. The Fortunate number for pn# is always above pn. This is because pn#, and thus pn# + m, is divisible by the prime factors of m for m = 2 to pn.The Fortunate numbers for the first primorials are:3, 5, 7, 13, 23, 17, 19, 23, 37, 61, 67, 61, 71, 47, 107, 59, 61, 109, etc. (sequence A005235 in OEIS).The Fortunate numbers sorted in numerical order with duplicates removed:3, 5, 7, 13, 17, 19, 23, 37, 47, 59, 61, 67, 71, 79, 89, 101, 103, 107, 109, 127, 151, 157, 163, 167, 191, 197, 199, ... ((sequence A046066 in OEIS)).Reo Fortune conjectured that no Fortunate number is composite. A Fortunate prime is a Fortunate number which is also a prime number. As of 2012, all the known Fortunate numbers are prime.".
- Fortunate_number wikiPageExternalLink page.php?sort=FortunateNumber.
- Fortunate_number wikiPageID "13040642".
- Fortunate_number wikiPageRevisionID "557576674".
- Fortunate_number hasPhotoCollection Fortunate_number.
- Fortunate_number title "Fortunate Prime".
- Fortunate_number urlname "FortunatePrime".
- Fortunate_number subject Category:Integer_sequences.
- Fortunate_number subject Category:Prime_numbers.
- Fortunate_number type Abstraction100002137.
- Fortunate_number type Arrangement107938773.
- Fortunate_number type DefiniteQuantity113576101.
- Fortunate_number type Group100031264.
- Fortunate_number type IntegerSequences.
- Fortunate_number type Measure100033615.
- Fortunate_number type Number113582013.
- Fortunate_number type Ordering108456993.
- Fortunate_number type Prime113594005.
- Fortunate_number type PrimeNumber113594302.
- Fortunate_number type PrimeNumbers.
- Fortunate_number type Sequence108459252.
- Fortunate_number type Series108457976.
- Fortunate_number comment "A Fortunate number, named after Reo Fortune, for a given positive integer n is the smallest integer m > 1 such that pn# + m is a prime number, where the primorial pn# is the product of the first n prime numbers.For example, to find the seventh Fortunate number, one would first calculate the product of the first seven primes (2, 3, 5, 7, 11, 13 and 17), which is 510510. Adding 2 to that gives another even number, while adding 3 would give another multiple of 3.".
- Fortunate_number label "Fortunate number".
- Fortunate_number label "Número afortunado".
- Fortunate_number label "フォーチュン数".
- Fortunate_number sameAs Número_afortunado.
- Fortunate_number sameAs フォーチュン数.
- Fortunate_number sameAs m.02z4bjh.
- Fortunate_number sameAs Q5151604.
- Fortunate_number sameAs Q5151604.
- Fortunate_number sameAs Fortunate_number.
- Fortunate_number wasDerivedFrom Fortunate_number?oldid=557576674.
- Fortunate_number isPrimaryTopicOf Fortunate_number.