SOLUTION: FIND AL NUMBERS LESS THAN 50THAT ARE PRIMES AND HAVE A REMAINDER OF 3 WHEN THEY ARE DIVIDED BY 7.

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Question 513810: FIND AL NUMBERS LESS THAN 50THAT ARE PRIMES AND HAVE A REMAINDER OF 3 WHEN THEY ARE DIVIDED BY 7.
Found 2 solutions by JBarnum, MathTherapy:
Answer by JBarnum(2146) (Show Source):
You can put this solution on YOUR website!
list all primes up to 50
1 2 3 5 7 11 23 29 31 37 41 43 47
1-7 easily cancel out
11 23 29 31 37 41 43 47
./.../.../...(31).../.../.../.../
7*4=28 28+3=31

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

FIND AL NUMBERS LESS THAN 50THAT ARE PRIMES AND HAVE A REMAINDER OF 3 WHEN THEY ARE DIVIDED BY 7.

Multiply all numbers, from 1 to 6, by 7, and than add 3 to see if the result is a prime number.

N.B. Multiplying 7 by 7, and adding 3 would yield 52 (7*7 + 3), which would be too large

_7 * 1 = 7 + 3 = 10 (NOT PRIME)
7 * 2 = 14 + 3 = 17 (PRIME)
7 * 3 = 21 + 3 = 24 (NOT PRIME)
7 * 4 = 28 + 3 = 31 (PRIME)
7 * 5 = 35 + 3 = 38 (NOT PRIME)
7 * 6 = 42 + 3 = 45 (NOT PRIME)
7 * 7 = 49 + 3 = 52 (NOT PRIME, and as stated above, 52 > 50)

Therefore, the numbers being sought are and

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