even, odd, and prime integers
... Fermat primes, defined as F[m]=2^2^m+1 for m=1, 2, 3, 4 lie along the line y=x in the first quadrant. Euler, and subsequent mathematicians, have shown that no Fermat primes exist for m=5 and higher. One recognizes from the above geometry that the odd numbers 8n+1, 8n+3, 8n+5 and 8n+7 along the diago ...
... Fermat primes, defined as F[m]=2^2^m+1 for m=1, 2, 3, 4 lie along the line y=x in the first quadrant. Euler, and subsequent mathematicians, have shown that no Fermat primes exist for m=5 and higher. One recognizes from the above geometry that the odd numbers 8n+1, 8n+3, 8n+5 and 8n+7 along the diago ...
Classic Open Problems in Number Theory
... There are infinitely many prime numbers. As such, there is no largest prime number. The probability that a large arbitrary integer n is prime is approximately 1/ln(n). As the size of integers increase, the probability that they are prime decreases; for example, the probability that a 500 digit integ ...
... There are infinitely many prime numbers. As such, there is no largest prime number. The probability that a large arbitrary integer n is prime is approximately 1/ln(n). As the size of integers increase, the probability that they are prime decreases; for example, the probability that a 500 digit integ ...
65. There`s always another prime
... don’t feature a single prime – consider the numbers from n! + 2 to n! + n, none of which can be prime. But do they ever peter out completely? ...
... don’t feature a single prime – consider the numbers from n! + 2 to n! + n, none of which can be prime. But do they ever peter out completely? ...
Theory Associated With Natural Numbers
... Each natural number n can be written as a product of prime numbers in one and only one way (except for the order of the factors). ...
... Each natural number n can be written as a product of prime numbers in one and only one way (except for the order of the factors). ...
Number Theory * Introduction (1/22)
... For any k > 2, are there any (non-trivial) solutions in natural numbers to the equation ak + bk = ck? If so, are there only finitely many, or are the infinitely many? This last problem is called Fermat’s Last Theorem. In general, equations in which we seek solutions in the natural numbers only are c ...
... For any k > 2, are there any (non-trivial) solutions in natural numbers to the equation ak + bk = ck? If so, are there only finitely many, or are the infinitely many? This last problem is called Fermat’s Last Theorem. In general, equations in which we seek solutions in the natural numbers only are c ...
