Prime numbers are integers that have no divisors except themselves and one. The sequence of primes begins 2, 3, 5, 7, 11, 13, 17, … and there are infinitely many. Below are ten examples of prime numbers that have unusual properties that you will not learn about in school. Tell your friends or your next [...]
Two famous unsolved problems in number theory are 1) Goldbach’s Conjecture, which claims that every even integer > 2 is expressible as the sum of two primes; and 2) de Polignac’s conjecture, which claims that every even integer can be expressed as the difference of two consecutive primes in infinitely many ways. As these famous [...]
The decimal expansion of p begins 3.14159265358 … and the number is defined as the ratio of a circle’s circumference to its diameter. If you fast forward to about the 760th digit in the decimal expansion of p, you will see the string “…34 999999 83…” That group of six repeating 9s in the center [...]
If you separate each of the digits of the number 8166 and form a sequence by summing them in a Fibonacci-like fashion thus: 8 + 1 + 6 + 6 = 21, 1 + 6 + 6 + 21 = 34, 6 + 6 + 21 + 34 = 67, …, after 14 terms you [...]
A palindrome is a number that reads the same way forward and backward. Examples are 1234321, 484, and 6300036. A number’s divisors are all the numbers that divide evenly into it. The divisors of 10, for example, are 1, 2, 5, and 10 because 10/1 = 10, 10/2 = 5, 10/5 = 2, and 10/10 [...]
It’s an uncertain world. No one knows from this day to the next what will happen or what to expect. Life itself is a gamble, and we play the odds everyday, irregardless of who those odds favor. However, we still want to know if the odds are in favor or against a certain event, such [...]
Square numbers. 12Â = 1, 22Â = 4, 32Â = 9, 42Â = 16, 52Â = 25, 62Â = 36 … They are one of the most basic classes of numbers. Many people consider a geometric square to be a perfect shape with the most pleasing type of symmetry, which brings us to the reason [...]
