• prime number
  Prime number
  A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
  
  
• twin prime
  Twin prime
  A twin prime is a prime number that differs from another prime number by two. Except for the pair , this is the smallest possible difference between two primes. Some examples of twin prime pairs are , , , , and...
  
   with 311
  311 (number)
  311 is the natural number after 310 and before 312.-In mathematics:311 is a twin prime with 313; an Eisenstein prime with no imaginary part and real part of the form 3n - 1; a Gaussian prime with no imaginary part and real part of the form 4n - 1; and a permutable prime with 113 and 131.It can be...
  
  
• centered square number
  Centered square number
  In elementary number theory, a centered square number is a centered figurate number that gives the number of dots in a square with a dot in the center and all other dots surrounding the center dot in successive square layers. That is, each centered square number equals the number of dots within a...
  
  
• long prime
• pythagorean prime
  Pythagorean prime
  A Pythagorean prime is prime number of the form 4n + 1. These are exactly the primes that can be the hypotenuse of a Pythagorean triangle.The first few Pythagorean primes are...
  
  
• regular prime
• palindromic prime
  Palindromic prime
  A palindromic prime is a prime number that is also a palindromic number. Palindromicity depends on the base of the numbering system and its writing conventions, while primality is independent of such concerns...
  
   in both decimal
  Decimal
  The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....
  
   and binary
  Binary numeral system
  The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...
  
  .
• truncatable prime
  Truncatable prime
  In number theory, a left-truncatable prime is a prime number which, in a given base, contains no 0, and if the leading digit is successively removed, then all resulting numbers are prime. For example 9137, since 9137, 137, 37 and 7 are all prime...
  
  
• happy number
• Armstrong number
  Narcissistic number
  In recreational number theory, a narcissistic number is a number that is the sum of its own digits each raised to the power of the number of digits. This definition depends on the base b of the number system used, e.g...
  
    - in base 4 ( 3×4² + 1×4¹ + 3×4⁰ = 3³ + 1³ + 3³ )

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