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For example, in the languages C, Java, C#, [2] Objective-C, and C++, (which use the same syntax in this case), the code fragment int x = 0 ; while ( x < 5 ) { printf ( "x = %d \n " , x ); x ++ ; } first checks whether x is less than 5, which it is, so then the {loop body} is entered, where the printf function is run and x is incremented by 1.
An example of a primitive recursive programming language is one that contains basic arithmetic operators (e.g. + and −, or ADD and SUBTRACT), conditionals and comparison (IF-THEN, EQUALS, LESS-THAN), and bounded loops, such as the basic for loop, where there is a known or calculable upper bound to all loops (FOR i FROM 1 TO n, with neither i ...
A prime sieve or prime number sieve is a fast type of algorithm for finding primes. There are many prime sieves. The simple sieve of Eratosthenes (250s BCE), the sieve of Sundaram (1934), the still faster but more complicated sieve of Atkin [1] (2003), sieve of Pritchard (1979), and various wheel sieves [2] are most common.
Ribenboim defines a triply palindromic prime as a prime p for which: p is a palindromic prime with q digits, where q is a palindromic prime with r digits, where r is also a palindromic prime. [5] For example, p = 10 11310 + 4661664 × 10 5652 + 1, which has q = 11311 digits, and 11311 has r = 5 digits. The first (base-10) triply palindromic ...
For example, a break statement would allow termination of an infinite loop. Some languages may use a different naming convention for this type of loop. For example, the Pascal and Lua languages have a "repeat until" loop, which continues to run until the control expression is true and then terminates. In contrast a "while" loop runs while the ...
However, infinite loops can sometimes be used purposely, often with an exit from the loop built into the loop implementation for every computer language, but many share the same basic structure and/or concept. The While loop and the For loop are the two most common types of conditional loops in most programming languages.
Let {q 1, q 2, …} be successive prime numbers in the interval (B 1, B 2] and d n = q n − q n−1 the difference between consecutive prime numbers. Since typically B 1 > 2, d n are even numbers. The distribution of prime numbers is such that the d n will all be relatively small. It is suggested that d n ≤ ln 2 B 2.
A prime number is a natural number that has exactly two distinct natural number divisors: the number 1 and itself. To find all the prime numbers less than or equal to a given integer n by Eratosthenes' method: Create a list of consecutive integers from 2 through n: (2, 3, 4, ..., n). Initially, let p equal 2, the smallest prime number.