# Write an algorithm and draw a flowchart of displaying first 1000 prime numbers

### Algorithm and flowchart to check prime number

Formal versus empirical[ edit ] Main articles: Empirical algorithmics , Profiling computer programming , and Program optimization The analysis, and study of algorithms is a discipline of computer science , and is often practiced abstractly without the use of a specific programming language or implementation. Different algorithms may complete the same task with a different set of instructions in less or more time, space, or ' effort ' than others. Now suppose you want to calculate the first prime numbers. Proof of program correctness by use of mathematical induction: Knuth demonstrates the application of mathematical induction to an "extended" version of Euclid's algorithm, and he proposes "a general method applicable to proving the validity of any algorithm". To determine whether a number is prime, it calls the function "IsThisNumberPrime" which is shown at the top of this page. It will allow you to open any chart and make modifications. Find the sum of all numbers, less than one million, which are palindromic in base 10 and base 2. For example, 5 is a prime number because you can divide 5 by 1 evenly and divide 5 by 5 without a remainder, but if you divide 5 by any other integer, you get a remainder. Euclid's original proof adds a third requirement: the two lengths must not be prime to one another.

Find the sum of the only eleven primes that are both truncatable from left to right and right to left. Similarly we can work from right to left:, 37, and 3. HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum.

E2: [Is the remainder zero? S, A, etc. Formal versus empirical[ edit ] Main articles: Empirical algorithmicsProfiling computer programmingand Program optimization The analysis, and study of algorithms is a discipline of computer scienceand is often practiced abstractly without the use of a specific programming language or implementation. This reduces the number of core instructions from thirteen to eight, which makes it "more elegant" than "Elegant", at nine steps. He defines "A number [to be] a multitude composed of units": a counting number, a positive integer not including zero.

## Write algorithm and draw flowchart to print prime numbers between 1 to 100

Another interesting case is the two relatively prime numbers and Now "Elegant" computes the example-numbers faster; whether this is always the case for any given A, B, and R, S would require a detailed analysis. From this follows a simple algorithm, which can be stated in a high-level description in English prose, as: High-level description: If there are no numbers in the set then there is no highest number. Use remainder r to measure what was previously smaller number s; L serves as a temporary location. The first few primes are quickly calculated, but as the primes get further apart the computation time increases. An inelegant program for Euclid's algorithm[ edit ] "Inelegant" is a translation of Knuth's version of the algorithm with a subtraction-based remainder-loop replacing his use of division or a "modulus" instruction. What is the largest n-digit pandigital prime that exists? How many circular primes are there below one million? Euclid stipulated this so that he could construct a reductio ad absurdum proof that the two numbers' common measure is in fact the greatest. Find the sum of the only eleven primes that are both truncatable from left to right and right to left.

Triangle, pentagonal, and hexagonal numbers are generated by the following formulae: Triangle. Heathwith more detail added. The name of the function is "IsThisNumberPrime. Knuth suggested You give the function a number and the output is "Yes" if the number is prime, or "No" if it is not.

## Algorithm to generate first 10 prime numbers

The flowchart above starts with the number 2 and checks each number 3, 4, 5, and so forth. What is the largest n-digit pandigital prime that exists? Further information: Euclid's algorithm The example-diagram of Euclid's algorithm from T. The name of the function is "IsThisNumberPrime. Different algorithms may complete the same task with a different set of instructions in less or more time, space, or ' effort ' than others. So, to be precise, the following is really Nicomachus' algorithm. You give the function a number and the output is "Yes" if the number is prime, or "No" if it is not. For example, 5 is a prime number because you can divide 5 by 1 evenly and divide 5 by 5 without a remainder, but if you divide 5 by any other integer, you get a remainder. An irrational decimal fraction is created by concatenating the positive integers: 0. The first ten pentagonal numbers are: 1, 5, 12, 22, 35, 51, 70, 92, , , Now "Elegant" computes the example-numbers faster; whether this is always the case for any given A, B, and R, S would require a detailed analysis. Methods have been developed for the analysis of algorithms to obtain such quantitative answers estimates ; for example, the sorting algorithm above has a time requirement of O n , using the big O notation with n as the length of the list.

When the counter hitsit stops the process.

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