SOLUTION: Find all the numbers less than 60 that are prime and have a remainder of 3 when they are divided by 7? Should have three answers but we only come up with two. Prime numbers less

Question 955487: Find all the numbers less than 60 that are prime and have a remainder of 3 when they are divided by 7? Should have three answers but we only come up with two.
Prime numbers less than 60: 2,3,5,7,11,13,17,23,29,31,37,41,43,47,54,59.
17/7 = 2.43
*19/7 = 2.71 round up = 3
*23/7 = 3.28 round = 3
29/7 = 4.14
31/7 = 4.42
What are we doing wrong.
Thank you,
t2newark

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
(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: ; so two numbers for sure that you are looking for 17.

What else?
.
Now your three numbers you were looking for are ----, 17, 31.

You missed 59.

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.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

Find all the numbers less than 60 that are prime and have a remainder of 3 when they are divided by 7? Should have three answers but we only come up with two.
Prime numbers less than 60: 2,3,5,7,11,13,17,23,29,31,37,41,43,47,54,59.
17/7 = 2.43
*19/7 = 2.71 round up = 3
*23/7 = 3.28 round = 3
29/7 = 4.14
31/7 = 4.42
What are we doing wrong.
Thank you,
t2newark

The easiest way to approach this is to add 3 to each MULTIPLE of 7 and then choose all those that are PRIME.
For example, 7(1) + 3 = 10 (Composite). After going through all the multiples of 7 that are less than 60,
you should get the 3 primes:
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