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Old 2018-02-26, 17:33   #1
Steve One
 
Feb 2018

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Default Prime counting function

PRIME NUMBER COUNTING: Eg: Up to 91squared and 121squared on number line (1+n30): 1,31,61,91 etc.

(A) 0.455897334 × (B)276 = 125.8255664157 (C) up to 91squared
(D) 0.430387657 × (E)488 = 210.0291769069 (F) up to 121 squared

B = (91squared - 1)/30.
C = Prime numbers up to 91squared on number line (1 + n 30) 1, 31, 61, 91 etc. which = 125(C)

E = (121squared - 1)/30
F = Prime numbers up to 121 squared on number line (1 + n30) 1, 31, 61 etc. which = 210(F)

A = (6 × 10 × 12 × 16 × 18 × 22 × 28 × 30 × 36 × 40 × 42 × 46 × 52 × 58 × 60 × 66 × 70 × 72 × 78 × 82 × 88)divided by (7 × 11 × 13 × 17 × 19 × 23 × 29 × 31 × 37 × 41 × 43 × 47 × 53 × 59 × 61 × 67 × 71 × 73 × 79 × 83 × 89)
OR
A = ((prime(1) - 1) × (prime(2) - 1)....× (prime(n) - 1)) divided by
((prime(1) × prime(2)......×.prime(n))
Prime 1 is 7. Prime 2 is 11. Prime 3 is 13 etc
Prime (n) in this case = 89(prime next down from 91)

D = A × ((96 × 100 × 102 × 106 × 108 × 112) divided by (97 × 101 × 103 × 107 × 109 × 113))
In this case prime (n) = 113(prime next down from 121).
There are more than 8 times as many primes up to 121 squared in totality because other number lines out of the possible 7+n30, 11+n30, 13+n30, 17+n30, 19+n30, 23+n30 and 29+n30, none except for above 1 + n30 use 112/113 and two don't use 108/109 which increases the number of primes on the number line.
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