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Every integer greater than 20161 can be written as the sum of two abundant numbers. The largest even number that is not the sum of two abundant numbers is 46. [5] An abundant number which is not a semiperfect number is called a weird number. [6] An abundant number with abundance 1 is called a quasiperfect number, although none have yet been found.
Write a computer program that sequentially tests this conjecture for increasing values. In the case of Goldbach's conjecture, we would consider every even number ≥ 4 sequentially and test whether or not it is the sum of two prime numbers. Suppose this program is simulated on an n-state Turing machine. If it finds a counterexample (an even ...
The first (base-10) triply palindromic prime is the 11-digit number 10000500001. It is possible that a triply palindromic prime in base 10 may also be palindromic in another base, such as base 2, but it would be highly remarkable if it were also a triply palindromic prime in that base as well.
All palindromic numbers with an even number of digits are divisible by 11. [ 1 ] There are 90 palindromic numbers with three digits (Using the rule of product : 9 choices for the first digit - which determines the third digit as well - multiplied by 10 choices for the second digit):
Histogram of total stopping times for the numbers 1 to 10 9. Total stopping time is on the x axis, frequency on the y axis. Iteration time for inputs of 2 to 10 7. Total stopping time of numbers up to 250, 1000, 4000, 20000, 100000, 500000. Consider the following operation on an arbitrary positive integer: If the number is even, divide it by two.
Thus if n is a large even integer and m is a number between 3 and n / 2 , then one might expect the probability of m and n − m simultaneously being prime to be 1 / ln m ln(n − m) . If one pursues this heuristic, one might expect the total number of ways to write a large even integer n as the sum of two odd primes to be roughly
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The number itself, which may appear in various places on the page, can be referred to as a page number or as a folio. [1] Like other numbering schemes such as chapter numbering, page numbers allow the citation of a particular page of the numbered document and facilitates to the reader to find specific parts of the document and to know the size ...