Palindromic prime

A Primzahlpalindrom is a prime number whose digits read from the front and from behind the same number shown analogously to the palindrome, read from the front and from behind which gives the same word. The Primzahlpalindrom is therefore a special Zahlenpalindrom.

Primzahlpalindrome depend from the base of the number system.

It is unknown whether there are infinitely many Primzahlpalindrome.

Explanation

If the prime number and the number of the prime number of the position where:

There is no decimal Primzahlpalindrome with an even number of locations in addition to the 11, because all Zahlenpalindrome have with an even number of digits of the divider 11 ( the alternating cross- sum is always 0). More generally applicable in all adic number system that if there ever is a Primzahlpalindrom with geradezahlig many places, this may be the only 11 of the corresponding number system.

Examples in number systems

Decimal

  • 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 10301, ... ( in sequence A002385 OEIS )
  • The largest known Primzahlpalindrom in decimal notation is 180005 decimal places, found in 2007 by Harvey Dubner.

Binary system

  • The largest known prime is the Mersenne prime number 243112609-1. In binary this is a column of ones 43,112,609 ones and thus - like every Mersenne number - a Zahlenpalindrom in the form of a binary ones column.
  • All Fermat primes are written in binary, Zahlenpalindrome. These are figures which have an odd number of zeros of a respective one to be framed. As the Mersenne primes Zahlenpalindrom property of the Fermat primes is not bound to the primary property, but applies to all Fermat numbers.

Strictly non-palindromic numbers

Numbers that can be written in any adic number system as Zahlenpalindrom > 11 are referred to as strictly non-palindromic numbers. All figures of this kind, which are > 6, are prime numbers. ( Sequence A016038 in OEIS )

Numeral system 101 (number)
661160
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