Prime Number R Program
Shanta Plansinis
A natural number is said to be prime if it is only divisible by itself and 1. In short, a prime number has only two factors that are 1 and the number itself. The numbers that are not prime are called composite numbers.
A prime number can be written as a product of only two numbers. For example, consider 3. Now, 3 can be written in the form of the product of two numbers in only one way i.e., 1 * 3. Whereas, 8 which is a composite number can be written as 1 * 8 and 2 * 4.
Now consider a prime integer 17. The factors of 17 are 1. After 17/2, i.e. 8.5 there is only one factor i.e. 17. So, to find if a number is prime or not, finding only one factor is enough. That one factor can be found in the first half, as you can notice that there is only one factor in the second half and i.e. the number itself.
This is a recursive approach to find the prime numbers. Here, a recursive function find_Prime is made that simply checks if the num is divisible by any number. If it is, then it returns false else the recursive call is made. This process repeats until any multiple of num is found.
In the above program, we are printing the sum of the prime numbers in the given range. The starting and ending points are being read by the user. We have iterated a nested for loop. The outer loop is running from the left till right and the inner loop is running up to n/2 for each iteration of the outer loop.
To wrap up, in this article, you have learned about the multiple ways to write a C program for prime numbers. You started with a quick introduction to prime numbers as well as some interesting facts about prime numbers.
While exploring the realm of programming, delving into algorithmic challenges such as creating a C program to check whether a number is prime can be both intriguing and enlightening. However, if you're aiming to broaden your horizons and master a suite of technologies that will prepare you for a versatile career in software development, considering a java full stack developer course might be your next strategic move.
Moving ahead, in the C program for Prime numbers article you saw different techniques to check for a prime number using for loops, while loops, functions, recursion, optimized method, etc. You learned how to print prime numbers within a range and one of the most popular methods called Sieves of Erastosthenes. You saw the algorithm, pseudocode, C program, time, and space complexities for each of the methods that we have discussed.
Version 30.19 is now available. ECM stage 2 is now much faster if you can give prime95 lots of memory to use. This is similar to the improvements to P-1 stage 2 in version 30.8. There are other minor bug fixes and tweaks. This is not a required upgrade -- version 30.3 and later can be used to hunt for new Mersenne primes. Should you decide to upgrade, if any workers are currently in ECM or P-1 stage 2 wait for ECM or P-1 to finish before upgrading. If you have any upgrade questions, ask in this thread at Mersenne Forum.
M(57885161) was discovered eight and half years ago. Now, thanks to the largely unheralded and dedicated efforts of thousands of GIMPS volunteers, every smaller Mersenne number has been successfully double-checked. Thus, M(57885161) officially becomes the 48th Mersenne prime. This is a significant milestone for the GIMPS project.
One year ago, first-time PRP primality testing with proofs was introduced. It has been a huge success, saving GIMPS tens of thousands future double-checks. Going forward, the server will no longer make available exponents for first time Lucas-Lehmer tests. Users that have not yet upgraded to prime95 version 30.3 or gpuowl for GPUs should do so. Failure to upgrade will result in unnecessary double-check work. GIMPS has a multi-year backlog of double-checks to work through. There is even a chance that a new Mersenne prime is hidden in all those double-checks.
For almost 25 years, GIMPS has looked for new Mersenne primes by running a primality test on one computer and later running the exact same primality test on another computer to guard against hardware errors having corrupted the first primality test.
A breakthrough by Krzysztof Pietrzak makes it possible to eliminate the second primality test! The first primality test produces a proof file that can be securely verified with less than 0.5% of the work required to re-run the primality test. This breakthrough will nearly double GIMPS' throughput in the long run.
Version 30.3 is now available with PRP proofs. While not a required upgrade, at some point in the future only users running version 30.3 with PRP proofs will be assigned first-time primality tests. Should you run into any problems, support is available at this thread at Mersenne Forum.
Many thanks to Mihai Preda for discovering the paper on the breakthrough and realizing its importance to the GIMPS project. Also, thanks go to Pavel Atnashev for important ideas on adapting the discovery for use by GIMPS.
SRBase has created a BOINC project to hand out trial factoring assignments on large Mersenne numbers. These are very quick work units. To get the most of the BOINC client without any issues, a FAQ at the SRBASE forum is available.
GIMPS has been on amazing lucky streak finding triple the expected number of new Mersenne primes -- a dozen in the last fifteen years. This prime was even luckier for Patrick Laroche, striking pay dirt on just his fourth try. For years, Patrick had used GIMPS software as a free "stress test" for his computer builds. Less than four months ago he started prime hunting on his media server to give back to the project. By way of comparison, some GIMPS participants have searched for more than 20 years with tens of thousands of attempts but no success. This proves that, with luck, anyone can find the next new Mersenne prime.
The new prime is only the 51st known Mersenne prime ever discovered. Mersenne primes were named for the French monk Marin Mersenne, who studied these numbers more than 350 years ago. GIMPS, founded in 1996, has discovered the last 17 Mersenne primes. Volunteers download a free program to search for these primes, with a cash award offered to anyone lucky enough to find a new prime. Prof. Chris Caldwell maintains an authoritative web site on the largest known primes, and has an excellent history of Mersenne primes.
Patrick is one of thousands of volunteers using free GIMPS software available at www.mersenne.org/download/. Credit for this prime goes not only to Patrick Laroche for running the Prime95 software, Woltman for writing the software, Blosser for keeping the Primenet server running smoothly, and the thousands of GIMPS volunteers that sifted through millions of non-prime candidates. In recognition of all the above people, official credit for this discovery goes to "P. Laroche, G. Woltman, A. Blosser, et al."
You could discover one of the most coveted finds in all of Mathematics - a new Mersenne prime number. We've found fifteen already. Join in on this fun, yet serious research project. All you need is a personal computer, patience, and a lot of luck.
In addition to the joy of making a mathematical discovery, you could win a (USD) $3,000 cash GIMPS Research Discovery Award for each Mersenne prime discovered, and the Electronic Frontier Foundation is offering a $150,000 award to the first person or group to discover a 100 million digit prime number! See how GIMPS will distribute this award if we are lucky enough to find the winning 100 million digit prime.
GIMPS, the Great Internet Mersenne Prime Search, was formed in January 1996 to discover new world-record-size Mersenne primes. GIMPS harnesses the power of thousands of small computers like yours to search for these "needles in a haystack".
I was trying to write a simple prime number program in Java 8. Below is the program. I wanted to reduce the code in isPrime() as well. Is there something that filters the elements from 2 to n/2, and then apply filter for n%i == 0 which would make isPrime irrelevant?
Your isPrime() is inefficient. First, you do not need to divide by any even numbers greater than 2, since an initial division by 2 will catch all even non-primes. Second, you terminate your loop at number / 2 instead of the more efficient sqrt(number).
iterate takes 3 parameters, similar to a for loop, base is the start, the second is the stop condition, third is the increment rule.1 and 2 are prime already so we start at 3 and we stop before reaching the square root of the number. The idea is that suppose n is a positive integer n=pq, where p and q are prime numbers. Assume p greater than square root of n and greater than square root of n. Multiplying these inequalities we have p*q > sqrt n * sqrt n, which implies pq > n. This is a contradiction to our hypothesis n=pq. Hence we can conclude that either p less or equal sqrt n or q less than equal sqrt n.
I am coming late to the game, but I am sharing my solution because there is a surprising number of incorrect implementations shared and the following code has better performance than the other boolean isPrime(int candidate) solutions.
The solution in the original post, the accepted answer, and many more answers are incorrect because they identify negative numbers, zero, and one as prime numbers, which they are not. See Wikipedia: _number
Since I don't have any hardware yet, I decided to do programming instead. I created a simple program that echoes a prime number every second, unless it took longer than a second to calculate it. (It would take an EXTREMELY long time to get that far.) The delay is editable. The program is 2548 bytes when compiled. It uses what is probably a well known algorithm to find prime numbers. (I just made it up, I'm sure this method already exists) I know it's not much, but it's the first thing I've ever done on an Arduino besides making a light blink, so I'm happy with it!
If a number is not prime, it will have factors that are prime, so if you want to get a lot more advanced and a lot faster, you can keep a table of all the primes you've already computed and iterate through those instead of testing every odd number every time. That gets into a programming technique called "dynamic programming".
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