Actually there is a formula to predict prime numbers. 1,2,3 aside you can predict them with the formula 6n+/-1

As said leaving 1,2 and 3 aside and also 6*0 where +/-1 one would be 1 and -1.

Next you take a look at 6*1 so 6.

6-1=5 which is prime and 6+1 you get 7 which is also prime.

Next look at 6*2=12

12–1=11 prime. 12+1=13 also prime

18–1=17 prime. 18+1=19 also prime

24–1=23 prime. 24+1=25 not prime

30–1=29 prime. 30+1=31 also prime

36–1=35 not prime. 36+1=37 which is prime

42–1=41 which is prime. 42+1=43 which is prime

48–1=47 which is prime. 48+1=49 which is not prime

54–1=53 which is prime. 54+1=55 which is not prime

60–1=59 which is prime. 60+1=61 which is also prime

66–1=65 not prime. 66+1=67 which is prime

72–1=71 prime. 72+1=73 prime

78–1=77 not prime. 78+1=79 prime

84–1=83 prime. 84+1=85 not prime

90–1=89 prime. 90+1=91 not prime

96–1=95 not prime. 96+1=97 prime

102–1=101 prime. 103 also prime

108–1=107 prime. 109 also prime

I guess you get the pattern and you can continue this list.

But lets make a jump here just looking at a list of prime numbers from 1–1000

for example:

6x138=828

828–1=827 prime. 828+1=829 also prime

834–1=833 not prime. 834+1=835 not prime

I wrote a programm in fortran that writes prime numbers into a file and counts them only looking for prime numbers at a position that is +/-1 of 6n by checking the usual stuff to determine if the number is prime or not and at last from 1–1,000,000,000 there was no prime number missing compared to results i found online. I stoped at 1,000,000,000 cause it takes quite a while calculating this but i’m also pretty sure that there are no existing prime numbers that are not next to a multiple of 6.

Sorry for the long text but you pointed out that there is no formula to predict a prime number.

But as far as i know and proofed this method works as i wasn’t able to find prime numbers somewhere else than next to a multiple of 6.

That also explains why there are so many pairs of prime numbers like 5 and 7 or 827 and 829 with this 2 as difference.

Greetings from Germany!

Daniel