Question

if p,8p-1 are primes then 8p+1is composite number when p is greater than are is equal to​

Answer 1

As for "where to start" on a question like this: I'd start by finding primes pp such that 8p−18p−1 is prime, and seeing if the prime factorizations of 8p+18p+1 have anything in common. A list of primes such as this one is useful. For p<100p<100, I find

3,23,25=5×53,23,25=5×5

13,103,105=3×5×713,103,105=3×5×7

19,151,153=32×1719,151,153=32×17

61,487,489=3×16361,487,489=3×163

79,631,633=3×21179,631,633=3×211

and from this you get the idea that if pp and 8p−18p−1 are both prime, then perhaps 8p+18p+1 must be divisible by 3.

So let pp be a prime such that 8p−18p−1 is also prime. If pp is prime, either p=3k+1p=3k+1 or p=3k−1p=3k−1 for some integer kk. (I'm omitting the p=3