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No composite number is a strong pseudoprime to all bases at the same time (contrary to the Fermat primality test for which Fermat pseudoprimes to all bases exist: the Carmichael numbers). However no simple way of finding a witness is known. A naïve solution is to try all possible bases, which yields an inefficient deterministic algorithm.
The major system (also called the phonetic number system, phonetic mnemonic system, or Hérigone's mnemonic system) is a mnemonic technique used to help in memorizing numbers. The system works by converting numbers into consonants, then into words by adding vowels. The system works on the principle that images can be remembered more easily than ...
Balanced ternary numeral system (base 3) Negative base numeral system (base −3) Quaternary numeral system (base 4) Quater-imaginary base (base 2 √ −1) Quinary numeral system (base 5) Pentadic numerals – Runic notation for presenting numbers; Senary numeral system (base 6) Septenary numeral system (base 7) Octal numeral system (base 8)
This means that the integer part of the natural logarithm of a number in base e counts the number of digits before the separating point in that number, minus one. The base e is the most economical choice of radix β > 1, [ 4 ] where the radix economy is measured as the product of the radix and the length of the string of symbols needed to ...
In mathematics a polydivisible number (or magic number) is a number in a given number base with digits abcde... that has the following properties: [1] Its first digit a is not 0. The number formed by its first two digits ab is a multiple of 2.
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There are 4842 strong pseudoprimes base 2 and 2163 Carmichael numbers below this limit (see Table 1 of [5]). Starting at 17·257, the product of consecutive Fermat numbers is a base-2 pseudoprime, and so are all Fermat composites and Mersenne composites.
The main difference between the Dominic system and the major system is the assignment of sounds and letters to digits. The Dominic system is a letter-based abbreviation system where the letters comprise the initials of someone's name, while the major system is typically used as a phonetic-based consonant system for either objects, animals, persons, or even words.