GENERATED PRIME NUMBERS.

The numerical value of polynomial   is a prime number for x = 0,1,2 … 40. Check it out in some cases (This famous formula due to Leonard Euler.)

The numerical value of polynomial  is a prime number for x = 0,1,2 … 80. Check it out in some cases.

MAGIC NUMBERS.

Take a three-digit number. Form the number obtained by writing to the right of the previous repeat number. This 6-digit number, divide it by 7 and the quotient obtained by 11 and the last quotient by 13 What is observed?

CURIOUS SERIE.

31, 331, 3331, 33331, 333331, 3333331, 33333331 are prime numbers

however no next:

333333331 = 17 · 19607843

PERFECT NUMBERS.

We would be difficult to find a set of numbers whose property and whose history were more fascinating (and more completely useless), or is found surrounded by the deepest mystery that the perfect numbers and their closest relatives, the friends numbers (Martin Garder.)

A number is perfect when it is equal to the sum of its divisors excluding same.

The less perfect number is 6 which is equal to the sum of its three dividers (1,2,3). The next is 28, the sum of 1,2,4,7 and 14.

Perfect numbers are given by the Euclides formula , where 2n-1 is a Mersenne number. The last discovered is 257885161-1(257885161-1) generated with the largest Mersenne known. see Mersenne primes.