Hi,
Based on these news stories that apparently shocked mathematicians:
Here is a new result I came up with that might be interesting related to this, and hopefully explain it. For all non negative integers x and for primorial 30 there are 8 equation sets that produce all primes except 2,3,5.
y = 30x + 1 y = 30x + 7 y = 30x + 11 y = 30x + 13 y = 30x + 17 y = 30x + 19 y = 30x + 23 y = 30x + 29
There always have to be a divisible by 4 number of these equation sets, since 1/4 of them produce all primes ending in 1,3,7,9 respectively. Ie: y = 30x + 1 (produces half of primes ending in 1) y = 30x + 7 (produces half of primes ending in 7) y = 30x + 11 (produces half of primes ending in 1) y = 30x + 13 (produces half of primes ending in 3) y = 30x + 17 (produces half of primes ending in 7) y = 30x + 19 (produces half of primes ending in 9) y = 30x + 23 (produces half of primes ending in 3) y = 30x + 29 (produces half of primes ending in 9)
So statistically it would make sense that these equations would be randomly distributed regarding their distribution of primes, so for any next prime each of the eight equations has a 1/8th probability of producing the next prime, but there is a 30 digit gap for the same equation to do this, which is more than the expected prime gap spacing up to reasonably large numbers, so really it is more likely for one of the 7 other different equations to produce the next prime, and only one of them has the same next digit 7, so the odds are the next digit will not be a repeating 7.
Simple proof! :D
cheers, Jamie