natural numbers

natural numbers by Thomas McClure I

Introduction

This is written on natural numbers.

II

natural numbers

[D. Wells. Prime Numbers, c. 2005] .... natural numbers split up into product of primes. {2001) (p. 242) J. R. Chen proved that every even number is the difference between a prime and a semiprime. (p. 218) [product of two primes] (p. 230) Let 2N = pq - p = p(q - 1) = 2pp 2p = (q - 1) Conjecture: every twice prime is a composite of prime minus one. Let the pair p and q be: {3,7}

6=6

{2,5}

4=4

{5,11}

10=10

{7,3*5}

14=14

{11,23}

22=22

{13,3*9}

26=26

{17,5*7}

34=34

{19,3*13} 38=38

Take the sum of p and the sum of q: [underline is median]

{10+18+30+19} = {40+37} = {7*11} {12+34+15+27+35+39} = {50+61+51} = {101+61} = {2*9*9} Take deviation from median:

{-9,-1,+11,0} {-15,+7,-12,0,+8,+12} Take sums of deviations: {+2} {+0} Take sums of squared deviations: {82+121} = {203} {225,49,64} = {338} Divide by range squared: {203/20*20} = {10.2 .../20} = {0.51..} {338/27*27} = {12.5.../27} = {0.46...} Take the product as a correlation: 0.2346 Then the equation of the sums of deviations: [0] = 0.2 * [2] p = 0.2 * q 10 p = 2 q 2*5*2 = 2*5 2 == 1 1==0

[unit circle]

Conjecture: (p-1) = 0.2(p+2) 10p - 10 = 2p + 4 8p = 14 p=3 24 = 14 1 = 0 mod 10 III

[unit circle base 10]

Conclusion

This is written on natural numbers.