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Wieferich primes: Difference between revisions

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Wieferich primes (view source)

Revision as of 20:30, 2 June 2021

3,501 bytes added ,  2 years ago
→‎{{header|Phix}}: added alternative, theoretically much faster
(Added Rust solution)
(→‎{{header|Phix}}: added alternative, theoretically much faster)
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=={{header|Phix}}==
 
<!--<lang Phix>(notonlinephixonline)-->
<span style="color: #008080;">include</span> <span style="color: #7060A8;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>▼
<span style="color: #7060A8008080;">mpzwith</span> <span style="color: #000000008080;">z</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()javascript_semantics</span>
<span style="color: #008080;">functioninclude</span> <span style="color: #000000004080;">wieferichmpfr</span><span style="color: #0000FF;">(.</span><span style="color: #004080;">integer</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">)e</span>
<span style="color: #7060A8008080;">mpz_set_strfunction</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">repeatweiferich</span><span style="color: #0000FF;">(</span><span style="color: #008000004080;">'1'integer</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
<span style="color: #008080004080;">returnmpz</span> <span style="color: #7060A8;">mpz_fdiv_q_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">zp2pm1m1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">*</span><span style="color: #0000007060A8;">pmpz_init</span><span style="color: #0000FF;">()=</span><span style="color: #000000;">0</span>
<span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p2pm1m1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpz_sub_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p2pm1m1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p2pm1m1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">mpz_fdiv_q_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p2pm1m1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p2pm1m1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">*</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"WieferichWeiferich primes less than 5000: %V\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">filter</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">get_primes_le</span><span style="color: #0000FF;">(</span><span style="color: #000000;">5000</span><span style="color: #0000FF;">),</span><span style="color: #000000;">wieferichweiferich</span><span style="color: #0000FF;">)})</span>
<!--</lang>-->
 
{{out}}
<pre>
Wieferich primes less than 5000: {1093,3511}
</pre>
alternative (same results), should be significantly faster, in the (largely pointless!) hunt for larger numbers.
<!--<lang Phix>(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
▲ <span style="color: #008080;">include</span> <span style="color: #7060A8004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
<span style="color: #004080;">mpz</span> <span style="color: #000000;">base</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">modulus</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">z</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_inits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">weiferich</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpz_set_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">modulus</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">*</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpz_powm_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">base</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">modulus</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">mpz_cmp_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Weiferich primes less than 5000: %V\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">filter</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">get_primes_le</span><span style="color: #0000FF;">(</span><span style="color: #000000;">5000</span><span style="color: #0000FF;">),</span><span style="color: #000000;">weiferich</span><span style="color: #0000FF;">)})</span>
<!--</lang>-->
 
=={{header|Raku}}==
Petelomax
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