Question

8. In how many pairs of consecutive prime mumbers from 1 to 100, does
a difference of 6 occur?

Answer 1

There are 7 such gaps of 6. A gap of 6 is one of the most common gaps in prime numbers. It is constructed from gaps of 2 and 4. Of the 7 gaps 5 of the gaps have a multiple the prime number 5 in the middle of them and the other 2 have a multiple of prime number 7 in the middle. The gaps with a multiple of 5 in the middle are (23, 29), (31, 37), (53, 59), (61, 67), (83, 89) and the multiple of 7 is in the middle of (47, 53), (73, 79), and one odd ball gap of 8 at (89, 97) which used both 5, and 7.

Answer 2

Step-by-step explanation:

primes_diff6.py 100 7 prime pairs found with a difference of 6. ( 23 , 29 ) ( 31 , 37 ) ( 47 , 53 ) ( 53 , 59 ) ( 61 , 67 ) ( 73 , 79 ) ( 83 , 89 ) 25 primes found.