# Math question - Prime Number Equation

by Lisa
(NJ)

Using the numbers 0, 2, 4, 3 , 5; put them into an equation and see if the result is a prime number.

### Comments for Math question - Prime Number Equation

 May 22, 2011 Prime Numbers by: Staff The question: by Lisa (NJ) Using the numbers 0, 2, 4, 3, 5; put them into an equation and see if the result is a prime number. The answer: 0,2,3,4,5 I’m unclear about what equation you are referring to. Are you referring to Wilson’s Theorem? The number n is prime if (n – 1)! + 1 = 0_mod_n There are only SIX prime numbers that can be formed using all of the 5 digits (0,2,3,4,5). They are: 02543, PRIME 04253, PRIME 04523, PRIME 20543, PRIME 40253, PRIME 50423, PRIME To be a 5 digit prime number, the LAST DIGIT must be an ODD number. There are only two odd numbers: 3 and 5 If the last digit is 5, the entire 5 digit number is divisible by 5 The only possibility left is using the 3 as the last digit. However, not all numbers ending the 3 are prime numbers. For example the number 63 ends in 3, but it is not a prime number since 63 can be divided by 3. A number is divisible by 3 if the sum of the digits is divisible by 3. In this case the sum of all the digits is: 0+2+3+4+5 = 14, which is not divisible by 3. So at least we know it is theoretically possible to form a prime number from the digits 0,2,3,4,5, as long as the last digit is 3. However, the other 4 digits 0,2,4,5 cannot be used randomly. 20453 is a not prime number since it can be divided by 113 These are only 24 possible arrangements of the first 4 digits. n! = 4*3*2*1 = 24 possibilities 0245 0254 0425 0452 0524 0542 2045 2054 2405 2450 2504 2540 4025 4052 4205 4250 4502 4520 5024 5042 5204 5240 5402 5420 These are the only possible arrangements of all five digits when the last digit is 3. 02453, divisible by 11 02543, PRIME 04253, PRIME 04523, PRIME 05243, divisible by 7 05423, divisible by 11 20453, divisible by 113 20543, PRIME 24053, divisible by 67 24503, divisible by 107 25043, divisible by 79 25403, divisible by 7 40253, PRIME 40523, divisible by 7 42053, divisible by 11 42503, divisible by 19 45023, divisible by 11 45203, divisible by 17 50243, divisible by 47 50423, PRIME 52043, divisible by 71 52403, divisible by 13 54023, divisible by 89 54203, divisible by 67 Thanks for writing. Staff www.solving-math-problems.com