World's Largest Known Prime Number

Euclid proved in the 3rd century BC that there are an infinite number of prime numbers. A prime number can be divided only by itself and the number 1. Primes serve as the building blocks for all positive integers, and have applications in cryptography and other fields.

Mersenne numbers are numbers that are one less than a power of two (2n – 1). A Mersenne number that is also a prime number is called a Mersenne prime. These can be found and verified relatively quickly. Before 1952, 12 Mersenne primes were known; with the aid of computers, 30 more have been found. The eight largest have all been found by the Great Internet Mersenne Prime Search (GIMPS), a distributed network of volunteers using their spare computer power to find the largest Mersenne primes.

The largest currently known prime, 243,112,609– 1, was found by electrical engineer Hans-Michael Elvenich on 6 Sept. 2008.

It has 12,978,189 digits.

General Notes : Prime Numbers for Exam Preparation

Prime Numbers General Notes

A prime number can be divided, without a remainder, only by itself and by 1. For example, 17 can be divided only by 17 and by 1.

Some facts:

1. The only even prime number is 2. All other even numbers can be divided by 2.
2. If the sum of a number's digits is a multiple of 3, that number can be divided by 3.
3. No prime number greater than 5 ends in a 5. Any number greater than 5 that ends in a 5 can be divided by 5.
4. Zero and 1 are not considered prime numbers.
5. Except for 0 and 1, a number is either a prime number or a composite number. A composite number is defined as any number, greater than 1, that is not prime.

To prove whether a number is a prime number, first try dividing it by 2, and see if you get a whole number. If you do, it can't be a prime number. If you don't get a whole number, next try dividing it by prime numbers: 3, 5, 7, 11 (9 is divisible by 3) and so on, always dividing by a prime number (see table below).

Here is a table of all prime numbers up to 1,000:

	2	3	5	7	11	13	17	19	23
29	31	37	41	43	47	53	59	61	67
71	73	79	83	89	97	101	103	107	109
113	127	131	137	139	149	151	157	163	167
173	179	181	191	193	197	199	211	223	227
229	233	239	241	251	257	263	269	271	277
281	283	293	307	311	313	317	331	337	347
349	353	359	367	373	379	383	389	397	401
409	419	421	431	433	439	443	449	457	461
463	467	479	487	491	499	503	509	521	523
541	547	557	563	569	571	577	587	593	599
601	607	613	617	619	631	641	643	647	653
659	661	673	677	683	691	701	709	719	727
733	739	743	751	757	761	769	773	787	797
809	811	821	823	827	829	839	853	857	859
863	877	881	883	887	907	911	919	929	937
941	947	953	967	971	977	983	991	997