Primorial primes: Difference between revisions

=={{header|Wren}}==

===Basic===

{{libheader|Wren-math}}

{{libheader|Wren-fmt}}

<lang ecmascript>import "./math" for Int

import "./fmt" for Fmt

var limit = 12

var c = 0

var i = 0

var primes = Int.primeSieve(99) // more than enough

var p = 1

System.print("First %(limit) primorial primes:")

while (true) {

if (Int.isPrime(p-1)) {

var pi = "p%(i)#"

Fmt.print("$2d: $4s - 1 = $d", c = c + 1, pi, p - 1)

if (c == limit) return

}

if (Int.isPrime(p+1)) {

var pi = "p%(i)#"

Fmt.print("$2d: $4s + 1 = $d", c = c + 1, pi, p + 1)

if (c == limit) return

}

p = p * primes[i]

i = i + 1

}</lang>

{{out}}

<pre>

First 12 primorial primes:

1: p0# + 1 = 2

2: p1# + 1 = 3

3: p2# - 1 = 5

4: p2# + 1 = 7

5: p3# - 1 = 29

6: p3# + 1 = 31

7: p4# + 1 = 211

8: p5# - 1 = 2309

9: p5# + 1 = 2311

10: p6# - 1 = 30029

11: p11# + 1 = 200560490131

12: p13# - 1 = 304250263527209

</pre>

===Stretch===

{{libheader|Wren-gmp}}

This takes about 53.4 seconds to reach the 30th primorial prime on my machine (Core i7) with the final one taking 35 seconds of this. Likely to be very slow after that as the next primorial prime is p1391# + 1.

<lang ecmascript>import "./gmp" for Mpz

import "./math" for Int

import "./fmt" for Fmt

var limit = 30

var c = 0

var i = 0

var primes = Int.primeSieve(9999) // more than enough

var p = Mpz.one

var two64 = Mpz.two.pow(64)

System.print("First %(limit) factorial primes:")

while (true) {

var r = (p < two64) ? 1 : 0 // test for definite primeness below 2^64

if ((p-1).probPrime(15) > r) {

var s = (p-1).toString

var sc = s.count

var digs = sc > 40 ? "(%(sc) digits)" : ""

var pn = "p%(i)#"

Fmt.print("$2d: $5s - 1 = $20a $s", c = c + 1, pn, s, digs)

if (c == limit) return

}

if ((p+1).probPrime(15) > r) {

var s = (p+1).toString

var sc = s.count

var digs = sc > 40 ? "(%(sc) digits)" : ""

var pn = "p%(i)#"

Fmt.print("$2d: $5s + 1 = $20a $s", c = c + 1, pn, s, digs)

if (c == limit) return

}

p.mul(primes[i])

i = i + 1

}</lang>

{{out}}

<pre>

First 30 factorial primes:

1: p0# + 1 = 2

2: p1# + 1 = 3

3: p2# - 1 = 5

4: p2# + 1 = 7

5: p3# - 1 = 29

6: p3# + 1 = 31

7: p4# + 1 = 211

8: p5# - 1 = 2309

9: p5# + 1 = 2311

10: p6# - 1 = 30029

11: p11# + 1 = 200560490131

12: p13# - 1 = 304250263527209

13: p24# - 1 = 23768741896345550770650537601358309

14: p66# - 1 = 19361386640700823163...29148240284399976569 (131 digits)

15: p68# - 1 = 21597045956102547214...98759003964186453789 (136 digits)

16: p75# + 1 = 17196201054584064334...62756822275663694111 (154 digits)

17: p167# - 1 = 19649288510530675457...35580823050358968029 (413 digits)

18: p171# + 1 = 20404068993016374194...29492908966644747931 (425 digits)

19: p172# + 1 = 20832554441869718052...12260054944287636531 (428 digits)

20: p287# - 1 = 71488723083486699645...63871022000761714929 (790 digits)

21: p310# - 1 = 40476351620665036743...10663664196050230069 (866 digits)

22: p352# - 1 = 13372477493552802137...21698973741675973189 (1007 digits)

23: p384# + 1 = 78244737296323701708...84011652643245393971 (1115 digits)

24: p457# + 1 = 68948124012218025568...25023568563926988371 (1368 digits)

25: p564# - 1 = 12039145942930719470...56788854266062940789 (1750 digits)

26: p590# - 1 = 19983712295113492764...61704122697617268869 (1844 digits)

27: p616# + 1 = 13195724337318102247...85805719764535513291 (1939 digits)

28: p620# - 1 = 57304682725550803084...81581766766846907409 (1953 digits)

29: p643# + 1 = 15034815029008301639...38987057002293989891 (2038 digits)

30: p849# - 1 = 11632076146197231553...78739544174329780009 (2811 digits)

</pre>