Factorial primes: Difference between revisions

=={{header|Racket}}==

<syntaxhighlight lang="racket">

#lang racket

(require gmp)

(define (factorial-boundary-stream)

(define (factorial-stream-iter n curr-fact)

(stream-cons `(- ,n ,(sub1 curr-fact))

(stream-cons `(+ ,n ,(add1 curr-fact))

(factorial-stream-iter (add1 n) (* curr-fact (+ n 1))))))

(factorial-stream-iter 2 2))

(define (format-large-number n)

(let* ([num-chars (number->string n)]

[num-len (string-length num-chars)])

(if (> num-len 40)

(string-append

(substring num-chars 0 19)

"..."

(substring num-chars (- num-len 19) num-len)

(format " (total ~a digits)" num-len))

n)))

(define (factorial-printer triple)

(let-values ([(op n fact) (apply values triple)])

(let ([fact (format-large-number fact)])

(displayln (format "~a! ~a 1 = ~a" n op fact)))))

(define (prime? n)

(not (zero? (mpz_probab_prime_p (mpz n) 10))))

(for ([i (in-stream

(stream-take

(stream-filter (λ (l) (prime? (third l))) (factorial-boundary-stream)) 30))]

[n (in-naturals 1)])

(begin

(display (format "~a:\t" n))

(factorial-printer i)))

;; time output of above code: 2.46 seconds

</syntaxhighlight>

<pre>

1: 2! + 1 = 3

2: 3! - 1 = 5

3: 3! + 1 = 7

4: 4! - 1 = 23

5: 6! - 1 = 719

6: 7! - 1 = 5039

7: 11! + 1 = 39916801

8: 12! - 1 = 479001599

9: 14! - 1 = 87178291199

10: 27! + 1 = 10888869450418352160768000001

11: 30! - 1 = 265252859812191058636308479999999

12: 32! - 1 = 263130836933693530167218012159999999

13: 33! - 1 = 8683317618811886495518194401279999999

14: 37! + 1 = 1376375309122634504...9581580902400000001 (total 44 digits)

15: 38! - 1 = 5230226174666011117...4100074291199999999 (total 45 digits)

16: 41! + 1 = 3345252661316380710...0751665152000000001 (total 50 digits)

17: 73! + 1 = 4470115461512684340...3680000000000000001 (total 106 digits)

18: 77! + 1 = 1451830920282858696...8000000000000000001 (total 114 digits)

19: 94! - 1 = 1087366156656743080...9999999999999999999 (total 147 digits)

20: 116! + 1 = 3393108684451898201...0000000000000000001 (total 191 digits)

21: 154! + 1 = 3089769613847350887...0000000000000000001 (total 272 digits)

22: 166! - 1 = 9003691705778437366...9999999999999999999 (total 298 digits)

23: 320! + 1 = 2116103347219252482...0000000000000000001 (total 665 digits)

24: 324! - 1 = 2288997460179102321...9999999999999999999 (total 675 digits)

25: 340! + 1 = 5100864472103711080...0000000000000000001 (total 715 digits)

26: 379! - 1 = 2484030746096470705...9999999999999999999 (total 815 digits)

27: 399! + 1 = 1600863071165597381...0000000000000000001 (total 867 digits)

28: 427! + 1 = 2906347176960734841...0000000000000000001 (total 940 digits)

29: 469! - 1 = 6771809666814951090...9999999999999999999 (total 1051 digits)

30: 546! - 1 = 1413020092614183254...9999999999999999999 (total 1260 digits)

cpu time: 2440 real time: 2440 gc time: 3</pre>