a,a+2,a+3 are three prime numbers .how many number of solutions can be made using this?

Answer 1

This has 1 solution
- 5, -3 ,-2

Note -ve number can be classified as prime or composite

Reason
No positive set

a cannot be odd then a+3 >+6 and even so it is not prime

a cannot be even then a has to be 2 and a+2 = 4 and it is not possible
similarly
no -ve set except the above
for -ve prime number please refer to the link

Answer 2

No solutions

If a=2, then a+2 = 4 which is not prime

If a=1 then a+3 = 4 which is not prime

Any other prime number must be odd, thus a+3 will be even and not prime.

Therefore, no solutions

Answer 3

No solutions.

(1) Prime numbers are GREATER THAN ONE, by definition.

(2) If 'a' is greater than 1, then one of (a+2) and (a+3) must be even, therefore not prime.