Pan base non-primes: Difference between revisions
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Percent odd up to and including 10000: 18.030657
Percent even up to and including 10000: 81.969343
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=={{header|PARI/GP}}==
{{trans|Mathematica/Wolfram_Language}}
<syntaxhighlight lang="parigp">
/* Define the function to check if a number is not prime in all bases greater than its maximum digit */
is_pan_base_composite(n) = {
my(d = digits(n), base, isComp);
for (base = vecmax(d)+1, max(n, 10),
isComp = !isprime(fromdigits(d, base));
if (!isComp, return(0)); /* If number is prime in any base, return false */
);
return(1); /* Number is composite in all bases */
}
/* Generate the list of all pan base composites up to 2500 */
pan_base_2500 = select(is_pan_base_composite, [2..2500]);
/* Define a function to check if a number is odd */
is_odd(n) = n % 2 == 1;
/* Filter out the odd numbers from the pan base composites */
odd_pan_base_2500 = select(is_odd, pan_base_2500);
/* Calculate the ratio of odd pan base composites to all pan base composites */
ratio = #odd_pan_base_2500 / #pan_base_2500;
/* Print the first 50 pan base non-primes */
print("First 50 pan base non-primes:");
print(concat("", vector(min(#pan_base_2500, 50), i, Str(pan_base_2500[i]))));
/* Print the first 20 odd pan base non-primes */
print("\nFirst 20 odd pan base non-primes:");
print(concat("", vector(min(#odd_pan_base_2500, 20), i, Str(odd_pan_base_2500[i]))));
/* Print the count of pan-base composites up to and including 2500 */
print("\nCount of pan-base composites up to and including 2500: ", #pan_base_2500);
/* Print the ratios */
default(realprecision, 4)
print("Odd up to and including 2500: ", ratio, ", or ", ratio * 100.0, "%.");
print("Even up to and including 2500: ", 1 - ratio, ", or ", (1 - ratio) * 100.0, "%.");
</syntaxhighlight>
{{out}}
<pre>
First 50 pan base non-primes:
["4", "6", "8", "9", "20", "22", "24", "26", "28", "30", "33", "36", "39", "40", "42", "44", "46", "48", "50", "55", "60", "62", "63", "64", "66", "68", "69", "70", "77", "80", "82", "84", "86", "88", "90", "93", "96", "99", "100", "110", "112", "114", "116", "118", "120", "121", "130", "132", "134", "136"]
First 20 odd pan base non-primes:
["9", "33", "39", "55", "63", "69", "77", "93", "99", "121", "143", "165", "169", "187", "231", "253", "273", "275", "297", "299"]
Count of pan-base composites up to and including 2500: 953
Odd up to and including 2500: 161/953, or 16.89%.
Even up to and including 2500: 792/953, or 83.11%.
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