Euler’s lucky number
A prime number is one of Euler’s lucky numbers if for each is also a prime. Put another way, a lucky number of Euler’s plus the th oblong number produces a list of primes -long. There are only six of them: 2, 3, 5, 11, 17 and 41, these are listed in A014556 of Sloane’s OEIS.
41 is perhaps the most famous of these. We can verify that 2 + 41 is 43, a prime, that 47 is also prime, so are 53, 61, 71, 83, 97, and so on to 1601, giving a list of 41 primes. Predictably, 1681 is divisible by 41, being its square. For the formula does not consistently give only composites or only primes.
|Title||Euler’s lucky number|
|Date of creation||2013-03-22 16:55:33|
|Last modified on||2013-03-22 16:55:33|
|Last modified by||PrimeFan (13766)|
|Synonym||lucky number of Euler|
|Synonym||Eulerian lucky number|