Num3er 1913

Paul Erdős   1913 – 1996

The year in which mathematician Paul Erdős was born is an emirp.
 

1913   is the smallest prime p such that its next prime (1931) is an anagram of p

An emirp (“prime” spelled backwards) is a prime whose (base 10) reversal is also prime, but which is not a palindromic prime.
http://mathworld.wolfram.com/Emirp.html

3191   is a prime number.

1913   is formed by the primes   19   and   13   or by the primes   191   and   3

1913   is a prime of the form   2 x^2 + 2 xy + 17 y^2
For   (-27, 7),   (-20, -7),   (20, 7),   (27, -7)

1913   is a prime of the form   16*n + 9     (n = 119)

1913   is a prime such that the sum of the predecessor and successor primes is divisible by 19
1907   and   1931   are the predecessor and successor primes.
1907   +   1931   =   19 * 202

1913   is a prime such that   3*p ± 2   are primes:
3*1913 – 2 = 5737    and    3*1913 + 2 = 5741
5737   and   5741   are primes.

 

1913   is
11101111001   in base 2
2121212   in base 3        (a palindrome)
131321   in base 4
30123   in base 5
12505   in base 6
5402   in base 7
3571   in base 8
2555   in base 9

 
1913   is deficient
1913   is evil :   it has an even number of 1’s in its binary expansion.
1913   is squarefree :
 
 
1913   =   8^2   +   43^2
 

1913   =   3^2   – 11^2   +   45^2
1913   =   – 3^2   + 31^2   +   31^2
1913   =   6^2   +   14^2   +   41^2
1913   =   – 6^2   +   10^2   +   43^2
1913   =   7^2   +   10^2   +   42^2
1913   =   – 7^2   +   21^2   +   39^2
1913   =   9^2   +   26^2   +   34^2
1913   =   – 9^2   +   25^2   +   37^2
1913   =   11^2   –   12^2   +   44^2
1913   =   11^2   –   18^2   +   46^2
1913   =   12^2   +   13^2   +   40^2
1913   =   12^2   –   16^2   +   45^2
1913   =   12^2   +   20^2   +   37^2
1913   =   14^2   +   14^2   +   39^2
1913   =   – 15^2   +   17^2   +   43^2
1913   =   16^2   +   19^2   +   36^2

 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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