Find the LAST Prime Number

Al Gore Rhythm
Al Gore Rhythm

July 3rd, 2014, 7:42 pm #1

It is easy to see that there are an infinite number of prime numbers, so there is no last prime with respect to the usual ordering 2,3,5,7, &c.

BUT..... We can order the prime numbers in alphabetical order according to their name in English (ignoring spaces and hyphens).

So "three" comes before "twenty-three" which comes before "two".

What is the *last* prime number in alphabetical order?

The names of the powers of ten are:

hundred, thousand, million, billion (10**9), trillion, quadrillion, quintillion, ..., decillion, undecellion, dodecillion, tredecillion, quattordecillion, ... vigintillion (10**63)

So the last prime should be close to two 2 x 10**63. (So you will need arbitrary precision math unless you want to use a list of prime numbers from the Internet).
You can use a probalistic primality test like Fermat's test.
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lawgin
lawgin

July 4th, 2014, 10:35 pm #2

Using the number descriptions that you provided, the highest number alphabetically would be:
two vigintillion two undecillion two trillion two thousand two hundred something.
Something would be an odd number between 1 and 99 if, indeed, any of these turn out to be prime.
Average spacing between primes at N is about equal to ln(N). ln(10^63) = 145 so it does seem quite possible that one of them would be prime.
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Anonymous
Anonymous

July 5th, 2014, 1:37 am #3

Scheme's bignum facility allows one to get the answer quickly (just run prime? in a loop) given this information.
Code for primality test in Scheme:

(define (expmod b e m)
(cond ((= e 1) b)
((even? e)
(remainder ((lambda (x) (* x x))
(expmod b (/ e 2) m)) m))
(else (remainder (* b (expmod b (- e 1) m)) m))))
;Value: expmod

(define (J a n)
(cond ((= a 1) 1)
((even? a) (* (J (/ a 2) n) (if (even? (/ (- (* n n) 1) 8))
1 -1)))
(else (* (J (remainder n a) a) (if (even? (/ (* (- a 1) (- n 1)) 4))
1 -1)))))
;Value: j

;; Solvay-Strassen test
(define (prime? n)
(define a (+ 2 (random (- n 2))))
(= (expmod a (/ (- n 1) 2) n) (J a n)))
;Value: prime?



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Anonymous
Anonymous

July 11th, 2014, 10:38 pm #4


in memorian der toxik von den vietnam strom problem

mini g~1


define (expmod b e m)
(cond ((= e 1) b)
((even? e)
(remainder ((lambda (x) (* x x))
(expmod b (/ e 2) m)) m))
(else (remainder (* b (expmod b (- e 1) m)) m))))
;Value: expmod

(define (J a n)
(cond ((= a 1) 1)
((even? a) (* (J (/ a 2) n) (if (even? (/ (- (* n n) 1) 8))
1 -1)))
(else (* (J (remainder n a) a) (if (even? (/ (* (- a 1) (- n 1)) 4))
1 -1)))))
;Value: j

;; Solvay-Strassen test
(define (prime? n)
(define a (+ 2 (random (- n 2))))
(= (expmod a (/ (- n 1) 2) n) (J a n)))
;Value: prime?
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der output ist


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if you give him a yes or no question

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(perhaps has the game in a workversion too
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