1. ## prime number

is this possible
if A is a prime number then A + 100 is also prime is A is not a part of the following series
2,5,8,11,14,17,20,23,26............
prove it also

2. Counterexample: $19$ is prime and is not included in the sequence $a_{n} = 2+3n$, but $119=7\cdot 17$ is not a prime...

Kind regards

$\chi$ $\sigma$

3. leaving 19 ,
is there a possibility

4. Further counterexample: $103 \ne 3n-1$ is prime, $203 = 7\cdot 29$ is not a prime...

Kind regards

$\chi$ $\sigma$

5. There are over 300 counter examples for numbers less than 10 thousand.