Below is a sample Java Program for Prime Number. Prime Number Program In Java Using. On my laptop machine running 3rd generation Core i7. Java program print prime numbers. Remember that smallest prime number is 2. Java programming code. Finding All Prime Numbers in the Range of 2. In mathematics, the sieve of Eratosthenes (Ancient Greek: Prime Numbers Generation in C++. If number is divided by any number that means it is not prime otherwise prime number. Here is the code of the Program. Prime number generator. This applet quickly generates a long list of prime numbers. If you were using a Java enabled browser the prime number generator would. C Program for Prime Number Generation. Training Program Will be held in A/C Hall & Reg.Fee includes Course Materials & Lunch. Some Basic and Inefficient Prime Number Generating Algorithms. Some Basic and Inefficient Prime Number Generating Algorithms. PGsimple. 1. This is considered to be a relatively easy task which is assigned within the first few weeks of the course. As I'm sure you are aware, a few simple and effective algorithms can be used to complete the assignment within as little as a few minutes. In the following examples, I will be using the Python. The first algorithm we shall consider will begin with the integer 2 and proceed to select each successive integer as a potential prime, (pp), checking for primacy by testing to see if it can be factored by any previously identified primes, then storing each newly verified prime in a prime set (ps) array. See Appendix A for a complete program including a user interface. Such a rudimentary algorithm takes a strictly brute force approach to effectively achieve the goal of identifying each prime number and storing it in an array. I am sure you would agree that this is also about the least efficient means of generating prime numbers. As we shall see, using elements of sieving processes will increase the efficiency of our program while avoiding the time consuming property of a true Sieve of Erastothenes which selects every consecutive integer as a potential prime before identifying it as factorable and eliminating it as a prime number, much the way PGsimple. Runtime Data. primes pgsimple. These are the best time results taken from 5 test runs at each limit. This table records the runtimes for pgsimple. Please accept that these runtimes and all of the runtimes given throughout this document may differ somewhat from those which you may get running the same program on a computer with different hardware or software as mine, which has an AMD Turion 6. GHz with 2. GB RAM, 1. GB HDD and Windows Vista. PGsimple. 2. It is most common to see such a device in algorithms which start with the integer 3 and proceed by selecting successive potential primes through the odd integers only. This reduces by half the total number of potential primes which must be tested. Note that the efficiency remains close to double that of pgsimple. Even at this speed, it is still quite impractical to generate 8 digit primes or more. But, I did it just to see how long it would take. PGsimple. 3? Note that the longer the program is run, the more significant the efficiency becomes. PGsimple. 4. Therefore, we can remove the first prime number from the set of primes which we test potential primes against. This requires dividing the prime set (ps) array into excepted prime (ep) and test prime (tp) arrays, then recombining them at the end to send the complete set back to the function call. Note that there is only a marginal increase in efficiency compared to pgsimple. Worry not, increases in efficiency multiply as more primes are eliminated from the testing process in the more advanced version of the program which I will show you next. This algorithm efficiently selects potential primes by eliminating multiples of previously identified primes from consideration and minimizes the number of tests which must be performed to verify the primacy of each potential prime. While the efficiency of selecting potential primes allows the program to sift through a greater range of numbers per second the longer the program is run, the number of tests which need to be performed on each potential prime does continue to rise, (but rises at a slower rate compared to other algorithms). Together, these processes bring greater efficiency to generating prime numbers, making the generation of even 1. PC. Further skip sets can be developed to eliminate the selection of potential primes which can be factored by each prime that has already been identified. Although this process is more complex, it can be generalized and made somewhat elegant. At the same time, we can continue to eliminate from the set of test primes each of the primes which the skip sets eliminate multiples of, minimizing the number of tests which must be performed on each potential prime. This example is fully commented, line by line, with some explanation to help the reader fully comprehend how the algorithm works. A complete program including a user interface, but without the comments, can be found in Appendix B. Please disregard syntactical errors which occur in the user interface such as . These errors can easily be corrected at the convenience of the student programmer, but were not necessary to illustrate the performance of the algorithms. I apologize for any confusion or inconvenience this may have caused the reader. This will be the upper limit of the test prime array for primes used to verify the primacy of any potential primes up to (lim). Primes greater than (sqrtlim) will be placed in an array for extended primes, (xp), not needed for the verification test. The use of an extended primes array is technically unnecessary, but helps to clarify that we have minimized the size of the test prime array. Although the value of the quantity of members in the skip set is never needed in the program, it may be useful to understand that future skip sets will contain more than one member, the quantity of which can be calculated, and is the quantity of members of the previous skip set multiplied by one less than the value of the prime which the new skip set will exclude multiples of. Example - the skip set which eliminates multiples of primes up through 3 will have (3- 1)*1=2 members, since the previous skip set had 1 member. The skip set which eliminates multiples of primes up through 5 will have (5- 1)*2=8 members, since the previous skip set had 2 members, etc. Future skip sets will have ranges which can be calculated, and are the sum of the members of the skip set. Another method of calculating the range will also be shown below. Also note that 3 is a verified prime, without testing, since there are no primes less than the square root of 3. This value is needed to define when to begin constructing the next skip set. Again, the use of an extended primes array is technically unnecessary, but helps to clarify that we have minimized the size of the test prime array. Note that 5 is a verified prime without testing, since there are no TEST primes less than the square root of 5. Otherwise, the potential prime variable is not changed and the current value remains the starting point for constructing the next skip set. Note that this is the case regardless of whether the next potential prime was verified as a prime, or not. Note that again the longer the program is run, the more significant the efficiency becomes. A note from the author. If you choose to translate this algorithm into another programming language, please email a copy of your work to cfo@mfbs. A note from the prime- number- best- algorithm owner. N+2. 9 or even better with 2. N+1, 2. 10. N+1. 1, 2. N+1. 3 ... 2. 10. N+2. 09. In short , use an algorithm to reduce the . Even so, numbers that have only factors which are larger than those base primes of the skip sets must be filtered by testing against primes greater than the filter primes, but less than the sqrt of the number being tested. Hence the need to generate at least all the primes up to the square root of the largest number to be tested. Enter y for yes or q to quit. Enter y for yes or q to quit.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. Archives
October 2016
Categories |