Question 915544: How many prime numbers between 8 and 60 leave a remainder of 2 when divided by 6?
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443)   (Show Source):
Answer by jim_thompson5910(35256)  (Show Source):
You can put this solution on YOUR website! List the prime numbers between 8 and 60
11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59
Now divide each prime number listed above by 6 and be sure to list the quotient and remainder
11/6 = 1 remainder 5
13/6 = 2 remainder 1
17/6 = 2 remainder 5
19/6 = 3 remainder 1
23/6 = 3 remainder 5
29/6 = 4 remainder 5
31/6 = 5 remainder 1
37/6 = 6 remainder 1
41/6 = 6 remainder 5
43/6 = 7 remainder 1
47/6 = 7 remainder 5
53/6 = 8 remainder 5
59/6 = 9 remainder 5
Notice how the remainders are either 1 or 5. None of the remainders are 2.
So the final answer is 0 because there are no primes in that list where you divide them by 6 to get a remainder of 2.
Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html
Thanks,
Jim
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