Wieferich primes: Difference between revisions

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sequences ;

"~~Weiferich~~ primes less than 5000:" print

"Wieferich primes less than 5000:" print

5000 primes-upto [ [ 1 - 2^ 1 - ] [ sq divisor? ] bi ] filter .</lang>

<pre>

~~Weiferich~~ primes less than 5000:

Wieferich primes less than 5000:

V{ 1093 3511 }

</pre>

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use ntheory 'is_prime';

say '~~Weiferich~~ primes less than 5000: ' . join ', ', grep { is_prime($_) and not ( (2**($_-1) -1) % $_**2 ) } 1..5000;</lang>

say 'Wieferich primes less than 5000: ' . join ', ', grep { is_prime($_) and not ( (2**($_-1) -1) % $_**2 ) } 1..5000;</lang>

<pre>~~Weiferich~~ primes less than 5000: 1093, 3511</pre>

<pre>Wieferich primes less than 5000: 1093, 3511</pre>

=={{header|Phix}}==

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include mpfr.e

mpz z = mpz_init()

function ~~weiferich~~(integer p)

function wieferich(integer p)

mpz_set_str(z,repeat('1',p-1),2)

return mpz_fdiv_q_ui(z,z,p*p)=0

end function

printf(1,"~~Weiferich~~ primes less than 5000: %V\n",{filter(get_primes_le(5000),~~weiferich~~)})

printf(1,"Wieferich primes less than 5000: %V\n",{filter(get_primes_le(5000),wieferich)})

<pre>

~~Weiferich~~ primes less than 5000: {1093,3511}

Wieferich primes less than 5000: {1093,3511}

</pre>

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=={{header|REXX}}==

<lang rexx>/*REXX program finds and displays ~~Weiferich~~ primes which are under a specified limit N*/

<lang rexx>/*REXX program finds and displays Wieferich primes which are under a specified limit N*/

parse arg n . /*obtain optional argument from the CL.*/

if n=='' | n=="," then n= 5000 /*Not specified? Then use the default.*/

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numeric digits max(9, length(2**n) ) /*calculate # of decimal digits needed.*/

call genP /*build array of semaphores for primes.*/

title= ' ~~Weiferich~~ primes that are < ' commas(n) /*title for the output. */

title= ' Wieferich primes that are < ' commas(n) /*title for the output. */

w= length(title) + 2 /*width of field for the primes listed.*/

say ' index │'center(title, w) /*display the title for the output. */

say '───────┼'center("" , w, '─') /* " a sep for the output. */

wp= 0 /*initialize number of ~~Weiferich~~ primes*/

wp= 0 /*initialize number of Wieferich primes*/

do j=1 to #; p= @.j; pm= p - 1 /*search for ~~Weiferich~~ primes in range.*/

do j=1 to #; p= @.j; pm= p - 1 /*search for Wieferich primes in range.*/

if (2**pm - 1) // p**2\==0 then iterate /*P**2 not evenly divide 2**(P-1) - 1?*/

wp= wp + 1 /*bump the counter of ~~Weiferich~~ primes.*/

wp= wp + 1 /*bump the counter of Wieferich primes.*/

say center(wp, 7)'│' center(commas(p), w) /*display the ~~Weiferich~~ prime to term. */

say center(wp, 7)'│' center(commas(p), w) /*display the Wieferich prime to term. */

end /*j*/

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<pre>

index │ ~~Weiferich~~ primes that are < 5,000

index │ Wieferich primes that are < 5,000

───────┼──────────────────────────────────────

1 │ 1,093

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───────┴──────────────────────────────────────

Found 2 ~~Weiferich~~ primes that are < 5,000

Found 2 Wieferich primes that are < 5,000

</pre>

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var primes = Int.primeSieve(5000)

System.print("~~Weiferich~~ primes < 5000:")

System.print("Wieferich primes < 5000:")

for (p in primes) {

var num = (BigInt.one << (p - 1)) - 1

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<pre>

~~Weiferich~~ primes < 5000:

Wieferich primes < 5000:

1093

3511