| Primorial |
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| CATEGORIES ABOUT PRIMORIAL | |
| integer sequences | |
| factorial and binomial topics | |
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For ''n'' ≥ 2, the primorial (''n''#) is the product of all Prime Number s less than or equal to ''n''. For example, 7# = 210 is a primorial which is the product of the first four primes multiplied together (2·3·5·7). The name is attributed to Harvey Dubner and is a Portmanteau of ''prime'' and '' Factorial ''. The first few primorials are : : 2 , 6 , 30 , 210, 2310, 30030, 510510, 9699690, 223092870, 6469693230, 200560490130, 7420738134810, 304250263527210, 13082761331670030, 614889782588491410. The idea of multiplying all primes occurs in a proof of the Infinitude Of The Prime Numbers ; it is applied to show a contradiction in the idea that the primes could be finite in number. Primorials play a role in the search for prime numbers in additive arithmetic progressions. For instance, 2236133941 + 23# results in a prime, beginning a sequence of thirteen primes found by repeatedly adding 23#, and ending with 5136341251. 23# is also the common difference in arithmetic progressions of fifteen and sixteen primes. Every Highly Composite Number is a product of primorials (e.g. 360 = 2·6·30). TABLE OF PRIMORIALS
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