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• Hello, please comment on below: take (Px)*(P1*P2*P3*...*Pn)+(Pn+1), (Px)*(P1*P2*P3*...*Pn)+(Pn+2), etc. where Px is a varying prime or 1 to get all primes.
Message 1 of 2 , Feb 18, 2006
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Hello,

take (Px)*(P1*P2*P3*...*Pn)+(Pn+1), (Px)*(P1*P2*P3*...*Pn)+(Pn+2), etc. where Px is a
varying prime or 1 to get all primes. e.g.

P1*P2*P3 = 2*3*5

now add Pn+1 = P4 = 30 + 7 = 37

P5 = 11, so => 41

continue:

13 => 43, 17 => 47, 19 => 49 (okay not prime so add again to 2*3*5 = 79 (in other words,
Px = 2, here))

continue:

23 => 53, 29 => 59, 31 => 61, 37 => 67, 41 => 71, 43 => 73, 47 => 77 (okay not prime so
add again to 2*3*5 = 107 (in other words, Px = 2, here))

continue:

53 => 83, 59 => 89, 61 => 91 (okay not prime so add again to 2*3*5 = 121 (okay still not
prime so add again to 2*3*5 = 151 (in other words, Px = 3, here)))

coninue:

67 => 97, 71 => 101, 73 => 103, 79 => 109 (but we already created this prime, so add
again FOUR MORE TIMES to 2*3*5 = 229 (in other words, Px = 5, here))

continue:

83 => 113, 89 => 119 (okay not prime so add again to 2*3*5 => 149 (Px = 2, here)

continue:

97 => 127, 101 => 131, 103 => 133, (okay not prime so add again to 2*3*5 => 163 (Px = 2,
here)

continue:

and so on ...

Bill

Bill Krys
Email: billkrys@...
Phone: 780.474.9493
Cell: (780) 995-6214
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• Hello Bill, your observation is well-known. It is simply because of the fact that by N=p1*p2*p3*... +px the p1, p2, p3… are excluded as prime divisors and
Message 2 of 2 , Mar 1, 2006
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Hello Bill,

your observation is well-known. It is simply because of the fact that
by N=p1*p2*p3*... +px the p1, p2, p3 are excluded as prime divisors
and therefore N with relatively large probability is prime. If N is
nevertheless not prime and you add 30 until it is prime, that is
because of the fact that after Dirichlet each arithmetic sequence of
the form a*n+b (thus also 30*n+N) contains infintitely many prime
numbers. Btw you may as well choose - instead of +: N=p1*p2*p3*... -px
and powers of p: N=p1^k1*p2^k2*p3^k3... + or - px^kx, where px^kx may
also be 1. By + or - you get a sort of symmetry in the distribution of
(small) prime numbers.

Werner
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