Lets start with the idea that every prime number except the number 2 is an odd number. Every odd number is either a Prime Number, or the result 2 Primes being multiplied together or the result of a Prime Number being multiplied with the result of two Primes being multiplied together
Examples of Primes Numbers that can only be divided by the number 1 and the number 1, 2, 5, 7,11 13 etc ( full chart at end of article)
Examples of numbers the result of primes being multiplied 3*3= 9, 3*5=15, 3*7=21, 5*5=25, 7*7=49 etc
Examples of Primes numbers being multiplied with the results of 2 primes being multiplied together 3*9=27, 3*15= 45, 3*21=63 etc
If we can identify and predict where there will be all the different kinds of Not Prime numbers then we find the Prime Numbers left over.
This is important because so far we cannot find out ahead of time if any number is a Prime Number nor find a pattern to find Prime Numbers unless we check to see if any number is a Prime Number first by using various mathamatical formulas.
My way is a first step in that direction I can find numbers that are not Prime.
My way starts at the number 1 and assumes its Prime same with the number 2 the fun starts with the number 3 multiple 3*3 and you get 9.
My theory assumes that every odd number between 3 and 9 then is Prime these numbers 5,7 can then be multiplied by the themselves and each other the odd numbers inbetween the numbers we find are Primes. Until we get to the number 9 the first number that is the result of 2 primes being multiplies together.
examples of multiples of Primes 3*3=9, 3* 5=15, 3*7=21
Next we add in the multiplies of Primes to the Prime numbers we multiply by themselves and with others numbers then what ever odd number is left is Prime
3 5 7 9 11 13 15 17 19
3 9
5 15 25
7 21 35 49
9 27 45 63 81
11 33 55 77 99
13 39 65 91 117 143 169
15 45 75 105 135 165 195 225
17 51 85 119 153 187 221 255 289
19 57 95 133 171 209 247 285 323 361
Arrrgh! I can’t get a chart with rows to work here!
Fine look at the numbers on the chart as I already stated 3*3=9 so every odd number inbetween 3 and 9 is Prime ( 5,7 ).
Next numbers are 9 and 15 on the chart the numbers 11 and 13 are indeed Prime.
15 and 21 the numbers inbetween 17 and 19 are indeed Prime.
Next step add to the top and left rows of the chart the Prime numbers that are inbetween the numbers in the center of the chart and start multiplying them to find more Prime Numbers at the same time add in the new numbers we find in the center of the chart to the left and top rows of the chart and start multiplying.
My theory does not prove a number is Prime it finds Prime Numbers with three acts of multiplication 3*3 and you get 9, 3* 5= 15, 3*7=21 I can find the Prime numbers 5,7, 11,13, 17 and 19.
For kids learning about Prime numbers or people working with paper and pencil or calculators it is helpful to create a chart like this instead of doing all the work of creating a chart of odd numbers to 100 and then removing all the multiples of Primes my way I think requires less work to find more Primes.
if you want to try to extend the chart yourself I will provide a list of Prime Numbers so you can check yourself below.
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67
71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163
167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269
271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383
389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499
503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619
631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751
757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881
883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997
http://www.mathsisfun.com/...