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