Answer to Question #42003 in Combinatorics | Number Theory for Janette
p = 6*(p/6) + (p%6),
where (p/6) is the integer quotient, and (p%6) is the modulo.
In general, the range of numbers for an integer modulo of n is 0 to n 1.
If p is a prime, this means p is divisible only by 1 and p. Since p is not divisible by 6, it would not leave a remainder of 0.
Also, a prime can not leave a remainder of 2, because then it would be divisible by 2:
p = 6*(p/6) + 2 = 2*(3*(p/6) + 1) and would not be a prime.
For the same reason, the remainder 3 and 4 are not possible.
Therefore, the possible modulos are 1 and 5.
Answer: 1, 5.
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