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What Is The Largest Prime Number Presently Known?

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enotes | (Level 1) Valedictorian

Posted October 9, 2011 at 4:00 PM via web

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What Is The Largest Prime Number Presently Known?

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fact-finder | (Level 3) Valedictorian

Posted October 10, 2011 at 4:00 PM (Answer #1)

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A prime number is a number other than 1, whose only divisors are 1 and itself—in other words, numbers (other than 1) with only two factors. Numbers with more than two factors are called composite numbers. (The number 1 is neither prime nor composite.) For example, the number 5 is prime because it is only divisible by 1 and itself. The number 6, which is divisible by 1, 2, 3, and 6, is composite. Other examples of prime numbers are: 2, 3, 7, 11,13, 17, and 19.

Ancient Greek mathematician Euclid (c. 330-c. 260 B.C.) proved that it is impossible to define a "largest prime number." This is because if you take the largest known prime number (P) and add 1 to the product of all primes up to and including P, you will get a number that is itself a prime number. For example, taking the prime number 7, you can multiply 2 x 3 x 5 x 7, and get 210. Adding 1 gives the number 211, which is prime.

In September 1997, Gordon Spence used a Pentium-based computer to determine the largest known prime number. The number, which is 895,932 digits long, is 22,976,221 -1.

Mathematicians since the days of Euclid have been trying, unsuccessfully, to find a pattern to the sequence of primes.

Sources: Motz, Lloyd, and Jefferson Hane Weaver. Conquering Mathematics, pp. 22-25; Science News, vol. 152, p. 164.

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nisarg | Student, Kindergarten | (Level 1) Valedictorian

Posted June 19, 2014 at 7:05 PM (Answer #2)

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22,976,221 -1

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