logo for solving-math-problems.com
leftimage for solving-math-problems.com

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

Click here to add your own comments

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



Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Math Questions & Comments - 01.



Copyright © 2008-2015. All rights reserved. Solving-Math-Problems.com