Conjectures

Two Conjectures I thought of.

  1. Every even number greater than zero is equal to the difference of two prime numbers
Ex. 
5 - 3 = 2
7 - 3 = 4
11 - 5 = 6
11 - 3 = 8
13 - 3 = 10
17 - 5 = 12
17 - 3 = 14
19 - 3 = 16
23 - 5 = 18
23 - 3 = 20
29 - 7 = 22
29 - 5 = 24
29 - 3 = 26
31 - 3 = 28
37 - 7 = 30
37 - 5 = 32
37 - 3 = 34
41 - 5 = 36
41 - 3 = 38
43 - 3 = 40
47 - 5 = 42
47 - 3 = 44
53 - 7 = 46
53 - 5 = 48
53 - 3 = 50
59 - 7 = 52
59 - 5 = 54
59 - 3 = 56
61 - 3 = 58
67 - 7 = 60
  1. There is an infinite number of differences of primes for every even number greater than zero
Ex. 
19 - 3 = 16
23 - 7 = 16
29 - 13 = 16
47 - 31 = 16
53 - 37 = 16
59 - 43 = 16
83 - 67 = 16
89 - 73 = 16
113 - 97 = 16
167 - 151 = 16
173 - 157 = 16
179 - 163 = 16
197 - 181 = 16
227 - 211 = 16
239 - 223 = 16
257 - 241 = 16
293 - 277 = 16
347 - 331 = 16
353 - 337 = 16
383 - 367 = 16
389 - 373 = 16
449 - 433 = 16
479 - 463 = 16
503 - 487 = 16
557 - 541 = 16
563 - 547 = 16
587 - 571 = 16
593 - 577 = 16
617 - 601 = 16
647 - 631 = 16
659 - 643 = 16
677 - 661 = 16
743 - 727 = 16
773 - 757 = 16
827 - 811 = 16
839 - 823 = 16
953 - 937 = 16
983 - 967 = 16