A Generalization of Fortune’s Conjecture
2014; Volume: 4; Issue: 2 Linguagem: Inglês
10.9734/bjmcs/2014/5701
ISSN2231-0851
Autores Tópico(s)History and Theory of Mathematics
ResumoFortune’s Conjecture is extended from a relatively short interval after each primorial # P to an infinite numbers of similar intervals on both sides of primorials # n P , where n is a positive integer. In addition, it is shown that for every prime y P in the interval ( ) 2 2 1 1 # , # j j j j n P P n P P + + − + ,there is a number x P in the interval ( ) 2 1 , j j P P + that is also a prime or 1, such that # y j x P n P P = ± . Since n can take infinitely many values, it is highly probable that the reverse of the above theorem is also true. Accordingly, it is conjecture that for every prime j P , there exist a prime x P in the interval ( ) 2 1 , j j P P + that gives a much larger prime when added to or subtracted from the primorial # j P multiplied by an integer n.
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