Define that the natural number p is a +1 prime of the natural number n if p is a prime number and the standard binary representation (i.e., without leading zeroes) of p can be obtained by adding (i.e., prepending, appending or inserting) a single 1 to the standard binary representation of n.
For example, the binary representation of 17 is 100012. The distinct natural numbers that can be formed by adding a 1 to 100012 are 1100012 or 49, 1010012 or 41, 1001012 or 37, and 1000112 or 35.
Among these, 41 and 37 are prime numbers, so 17 has two +1 primes.
Write a program or function that accepts a strictly positive integer n as input and prints or returns the number of distinct +1 primes of n.
Input and output must either be an integer, or its decimal or unary string representation.
Standard code-golf rules apply.
Input: 4 Output: 0 Input: 1 Output: 1 Input: 17 Output: 2 Input: 33 Output: 3 Input: 553 Output: 4 Input: 3273 Output: 5 Input: 4145 Output: 6 Input: 4109 Output: 7 Input: 196869 Output: 8