Fun with numbers - Generating prime numbers

 

It P.Q are two different prime numbers with different  digital ending , then  in most  cases

P + Q + PQ  becomes  a generator of  new prime 

3+5 +15 = 23

3+ 7 + 21 = 31

3 + 11 + 33 = 47

                               3 + 13 + 39 = 55

3 + 17 + 51 = 71

3 + 19 + 57 = 79

                               3 + 23 + 69 = 95

                               3 + 29 + 87 =119 

3 + 31 + 93=127

 

5 + 7 = 35 = 47

5+11+55 =71

5 + 13 + 65 = 83

5 + 17 + 85 = 107

                                5 + 19 + 95 = 119

The  P and Q may be one odd and another even. If the even number is 2, the only even prime number,, then P + Q + PQ in most cases is prime. In the form (5 + 6n)

2 + 1 +2 = 5

2+ 3 + 6  = 11

2+5 +10 = 17

2+7 + 14 = 23

2+ 9 + 18 = 29

                                2 + 11 + 22 = 35  

2+13 + 26 = 41

2 +15 +30 = 47

2+17 + 34= 53 

When the even number is 4, the generated primes are in the form  (9 +10n)

                               4 + 1 + 4 = 9

4 + 3 +12 = 19

4+5 +20 = 29

                                   4+7+2 8 = 39  

4+9 +36 = 49

4+11+44 =59