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# Re: Why tuples only to 22?

Tue, 2009-02-17, 15:23

Ricky Clarkson wrote:

>

> What would you consider a more usual cutoff point?

>

23 would be just right, according to this documentary film:

http://movies.yahoo.com/movie/1809356682/details

;->

Jeff Grigg wrote:

>

>

> Ricky Clarkson wrote:

>>

>> What would you consider a more usual cutoff point?

>>

>

> 23 would be just right, according to this documentary film:

> http://movies.yahoo.com/movie/1809356682/details

>

> ;->

>

There is no prime in which the mean gap between the first n successive

primes is exactly 22.

It is unknown if there is a relatively prime pair of amicable numbers. If

there is such a pair, their product must be at least 22 distinct primes.

The smallest integer such that its sum of digits + 1 and the product of its

digits is prime, together with the fact that the sum of digits is the same

as the product.

22 is the smallest number which can be expressed as the sum of two primes in

three ways.

1^pi(1) + 2^pi(2) + 3^pi(3) + 4^pi(4) + ... + 22^pi(22) is prime.

The smallest multi-digit square-free number such that all the digits are

primes.

The smallest multi-digit composite palindrome whose total number of prime

factors (counting multiplicity) is square-free.

The longest known arithmetic sequence of primes is currently 22, starting

with the prime 11410337850553 and continuing with common difference

4609098694200 (found by Pritchard, Moran, and Thyssen in 1993).

22 is the smallest multidigit composite palindrome such that the

concatenation (211) as well as the sum (13) of its prime factors are prime.

It is possible for a Queen to attack all 22 prime numbered squares on 9x9

Knight's Tour solution.

22 is the smallest Hoax Number.

The smallest dihedral semiprime. Note that it contains the smallest dihedral

prime.

(from http://primes.utm.edu/curios/page.php?short=22 Prime Curious! )