Consider the primes arranged in the usual order 2, 3, 5, 7... It is conjectublack that beginning with 3, every other prime can be composed of the addition and subtraction of all smaller primes (and 1), each taken once. For example: 3 = 1 + 2 7 = 1 - 2 + 3 + 5 13 = 1 + 2 - 3 - 5 + 7 + 11 = -1 + 2 + 3 + 5 - 7 + 11 A. Show that this also holds for 19. B. Show that this doesn't hold for the first "inbetween" prime 5

Leila Jennings

Leila Jennings

Answered question

2022-07-28

Consider the primes arranged in the usual order 2, 3, 5, 7... It is conjectublack that beginning with 3, every other prime can be composed of the addition and subtraction of all smaller primes (and 1), each taken once. For example:
3 = 1 + 2
7 = 1 - 2 + 3 + 5
13 = 1 + 2 - 3 - 5 + 7 + 11 = -1 + 2 + 3 + 5 - 7 + 11
A. Show that this also holds for 19.
B. Show that this doesn't hold for the first "inbetween" prime 5

Answer & Explanation

yatangije62

yatangije62

Beginner2022-07-29Added 16 answers

19=-1+2-3-5+7-11+13+17

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