2^(p-1) *(2^(p)-1)
A perfect number is a number which equals 1/2 the sum of all its positive integer divisors. Euclid proved that for the perfect number to be even, p must be prime. The first perfect number is 6. (1/2)(1+2+3+6)= 12/2= 6. In this case, p=2
2^(2-1) *(2^(2)-1)= 2 *3= 6
By research, the fifth perfect number is 33,550,336 and p= 13
33,550,336 = 2^(p-1) *(2^(p)-1)
33,550,336 = 2^(13-1) *(2^(13)-1)
33,550,336 = 2^12 * (2^13 -1) = 4096 *8191 = 33,550,336
Note that p is prime here.
A perfect number is a number which equals 1/2 the sum of all its positive integer divisors. Euclid proved that for the perfect number to be even, p must be prime. The first perfect number is 6. (1/2)(1+2+3+6)= 12/2= 6. In this case, p=2
2^(2-1) *(2^(2)-1)= 2 *3= 6
By research, the fifth perfect number is 33,550,336 and p= 13
33,550,336 = 2^(p-1) *(2^(p)-1)
33,550,336 = 2^(13-1) *(2^(13)-1)
33,550,336 = 2^12 * (2^13 -1) = 4096 *8191 = 33,550,336
Note that p is prime here.