Primorial primes: Difference between revisions
Content added Content deleted
Thundergnat (talk | contribs) m (remove task markup so it doesn't get indexed) |
Thundergnat (talk | contribs) m (convert to a redirect) Tag: New redirect |
||
| Line 1: | Line 1: | ||
| ⚫ | |||
{{alertbox|pink|Please do not add new examples to this page. |
|||
| ⚫ | |||
Please merge examples here with that page pending deletion. At least one language example exists here but not there.}} |
|||
;Definition |
|||
A [[wp:Primorial_prime|'''primorial prime''']] is a prime number that is one less or one more than a [[wp:Primorial|primorial]]. |
|||
In other words a non-negative integer '''n''' corresponds to a primorial prime if either '''pn'''# - 1 or '''pn'''# + 1 is prime where '''pn'''# denotes the product of the first '''n''' primes. |
|||
;Examples |
|||
4 corresponds to the primorial prime p4# + 1 = 2 x 3 x 5 x 7 + 1 = 211. |
|||
6 corresponds to the primorial prime p6# - 1 = 210 x 11 x 13 - 1 = 30029. |
|||
;Task |
|||
Find and show here the first 12 primorial primes. As well as the prime itself show the primorial number '''pn''' to which it corresponds and whether 1 is to be added or subtracted. |
|||
As p0# (by convention) is 1 and p1# is 2, start counting from p0#. |
|||
;Stretch |
|||
If your language supports arbitrary sized integers, do the same for at least the next 12 primorial primes. |
|||
As it can take a long time to demonstrate that a large number (above say 2^64) is definitely prime, you may instead use a function which shows that a number is probably prime to a reasonable degree of certainty. Most 'big integer' libraries have such a function. |
|||
If a number has more than 40 digits, do not show the full number. Show instead the first 20 and the last 20 digits and how many digits in total the number has. |
|||
;References |
|||
* [[oeis:A228486|OEIS:A228486 - Primorial primes]] |
|||
* [[oeis:A057704|OEIS:A057704 - Primorial - 1 prime indices]] |
|||
* [[oeis:A014545|OEIS:A014545 - Primorial + 1 prime indices]] |
|||
;Related task |
|||
* [[Factorial_primes|Factorial primes]] |
|||
<br><br> |
|||
=={{header|Factor}}== |
|||
{{works with|Factor|0.99 2022-04-03}} |
|||
<lang factor>USING: formatting kernel math math.factorials math.parser |
|||
math.primes sequences ; |
|||
: .p ( n i sgn p -- ) |
|||
[ >dec "p" "#" surround ] 2dip |
|||
"%2d:%6s %s 1 = %d\n" printf ; |
|||
[let |
|||
1 0 :> ( i! p! ) |
|||
[ i 12 <= ] [ |
|||
p primorial 1 - :> a |
|||
a 2 + :> b |
|||
a prime? [ i p "-" a .p i 1 + i! ] when |
|||
b prime? [ i p "+" b .p i 1 + i! ] when |
|||
p 1 + p! |
|||
] while |
|||
]</lang> |
|||
{{out}} |
|||
<pre> |
|||
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> |
|||
=={{header|J}}== |
|||
Compare with the [[Factorial_primes#J|j factorial prime]] implementation. |
|||
Columns here are primorial prime number cardinal number, primorial prime, primorial index number, and offset from the corresponding primorial to the prime: <lang J> P=: 1,*/\ p:i.15 NB. primorials represented as fixed width 64 bit integers |
|||
(,.~ #\)(,. (-{&P)/"1) (,. P I. <:) /:~(#~ 1 p: ]) ,P+/1 _1 |
|||
1 2 0 1 |
|||
2 3 1 1 |
|||
3 5 2 _1 |
|||
4 7 2 1 |
|||
5 29 3 _1 |
|||
6 31 3 1 |
|||
7 211 4 1 |
|||
8 2309 5 _1 |
|||
9 2311 5 1 |
|||
10 30029 6 _1 |
|||
11 200560490131 11 1 |
|||
12 304250263527209 13 _1</lang> |
|||
Latest revision as of 10:56, 12 September 2022
Redirect to: