Elementary arithmetic, with brief notices of its history... by Robert Potts.

5
4. PROP. In the series of the natursal nimbers (t leastfor the first 1000)
the prime numbers do not occur in any regular order of sequence in any
classes into which the natural numbers can be divided, as )may be seen from
the following table, which contaias the prime numbers in the frst 1000
natural numbers:1 -1 79 193 317 457 599 727 859
2 83 197 331 461 301 733 863
3 89 199 337 463 607 739 877
5 97 211 347 467 613 743 881
7 101 223 349 479 617 751 883
11 103 227 353 487 619 757 887
13 107 229 359 491 631 761 907
17 109 233 367 499 641 769 911
19 113 239 373 503 643 773 919
23 127 241 379 509 647 787 929
29 131 251 383 521 653 797 937
31 137 257 389 523 659 809 911
37 139 263 397 541 661 811 94,7
41 149 269 401 547 673 821 953
43 151 271 409 557 677 823 967
47 157 277 419 563 683 827 971
53 163 281 421 569 691 829 977
59 167 283 431 571 701 839 983
61 173 293 433 577 709 853 991
67 179 307 439 587 719 857 997
71 181 311 443 593
73 191 313 449
5. PnOP. 2o find the pr;ime factors of a given composite znu)ber.2
As every composite number consists of the product of prime
numbers, hence, if the given composite number be successively
divided, as often as possible, by each of the prime numbers, beginning with the least by which the given number is divisible, until the
1 If the natural numbers be formed into classes by tens, hundreds, &c., it will
be found that the prime numbers do not occur in any regular order, either in the
classes or in the order of the natural numbers.
2 Resolve the number 32760 into its prime factors:
Here 32760 divided by 2 gives quotient 16380, or 2)S2760
16880,, 2,, 8190,, 2)16380
8190,, 2,, 4095,, 2)8190
4095,, 3, 1365,, 3)4095
1365,, 3,, 455,, 3)1365
455.,, 5, 91,, 5)455
91,, 7,, 13,, 7)91
13,, 13, 1, 13)13
The divisors 2, 2, 2, 3, 3, 5, 7, 13, are the prime factors of 32760.
And 32760=2X2X2X3X3X5X7X13, or=23X32X5X7X13.