Question 955487
(FIXED MISTAKE in earlier solution)


Your list of prime numbers is wrong.

PRIMES LESS THAN 60:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59.


You could to decide to include 3, because the whole part of the quotient 3/7 is 0; and the remainder is obviously 3.


-------------.


Something else:  {{{17/7=2&3/7}}}; so two numbers for sure that you are looking for  17.


What else?
{{{31/7=(28+3)/7=28/7+3/7=4+3/7}}}.
Now your three numbers you were looking for are ----, 17, 31.


You missed 59.

{{{59/7=8&3/7}}}
Meaning there are FOUR prime numbers less than 60 which when divided by 7 give a remainder of 3; they are:
------just these--------17, 31, 59.