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Note- All primes greater than 3 can be written as 6n+1 or 6n-1

But all numbers in the form of 6n+1 or 6n-1 are not primes.

https://primes.utm.edu/notes/faq/six.html

Not all primes greater than 3 can be written as 6n+1 or 6n-1

example: 120=6x20. 120-1=119 which is divisble by 7. 120+1=121 which is divisible by 11.