User:PGP73

Permutable prime index of a prime

Assumption: decimal numbers since we call out to exclude numbers ending in 5. base is not an issue in general.

Take a prime number and get all the permutations of its digits. Remove any numbers ending in 0, 2, 4, 6, 8 and 5.

Permuted prime index is the count of primes within these candidates divided by the count of candidates.

Eg: 4751

Number of digits: 4

Permutations: 4! = 24

Ending exclusions: 4, 5

Acceptable permutations: 24 - ( 2 x 6 )= 12

1 1457 31 x 47

2 1547 13 x 17

3 4157 prime

4 4517 prime

5 4571 7 x 653

6 4751 prime

7 5147 prime

8 5417 prime

9 5471 prime

10 5741 prime

11 7451 prime

12 7541 prime

For 4751, the PPI is 9/12 = 0.75

37 is a number with PPI = 1.

Number of digits: 2

Permutations: 2! = 2

Ending exclusions: 0

Acceptable permutations: 2

37 prime

73 prime

PPI is 2/2 = 1