Pan base non-primes: Difference between revisions
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Percent even up to and including 10000: 81.969343
</pre>
=={{header|EasyLang}}==
<syntaxhighlight>
fastfunc isprim num .
if num mod 2 = 0
if num = 2
return 1
.
return 0
.
if num mod 3 = 0
if num = 3
return 1
.
return 0
.
i = 5
while i <= sqrt num
if num mod i = 0
return 0
.
i += 2
if num mod i = 0
return 0
.
i += 4
.
return 1
.
proc digits n . d[] .
while n > 0
d[] &= n mod 10
n = n div 10
.
.
proc fromdigits b . d[] n .
n = 0
for i = len d[] downto 1
n = n * b + d[i]
.
.
func panbasenpr n .
if n < 10
return 1 - isprim n
.
if n > 10 and n mod 10 = 0
return 1
.
digits n d[]
for i to len d[]
if maxdig < d[i]
maxdig = d[i]
.
.
for base = maxdig + 1 to n
fromdigits base d[] n
if isprim n = 1
return 0
.
.
return 1
.
print "First 50 prime pan-base composites:"
n = 2
repeat
if panbasenpr n = 1
cnt += 1
write n & " "
.
until cnt = 50
n += 1
.
cnt = 0
print "\n\nFirst 20 odd prime pan-base composites:"
n = 3
repeat
if panbasenpr n = 1
cnt += 1
write n & " "
.
until cnt = 20
n += 2
.
limit = 10000
cnt = 0
for n = 2 to limit
if panbasenpr n = 1
cnt += 1
if n mod 2 = 1
odd += 1
.
.
.
print "\nCount of pan-base composites up to and including " & limit & ": " & cnt
p = 100 * odd / cnt
print "Percent odd up to and including " & limit & ": " & p
print "Percent even up to and including " & limit & ": " & 100 - p
</syntaxhighlight>
=={{header|J}}==
Line 582 ⟶ 680:
Odd up to and including 2500: 161//953, or 16.89%.
Even up to and including 2500: 792//953, or 83.1%.
</pre>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
{{trans|Julia}}
<syntaxhighlight lang="Mathematica">(* Define the function to check if a number is a pan base composite *)
IsPanBaseComposite[n_] := Module[
{d = IntegerDigits[n], bases, compositeInAllBases},
bases = Range[Max[d] + 1, Max[10, n]];
compositeInAllBases = Not /@ PrimeQ[FromDigits[d, #] & /@ bases];
AllTrue[compositeInAllBases, Identity]
]
(* Generate the list of all pan base composites up to 2500 *)
panBase2500 = Select[Range[2, 2500], IsPanBaseComposite]
(* Filter out the odd numbers from the pan base composites *)
oddPanBase2500 = Select[panBase2500, OddQ]
(* Calculate the ratio of odd pan base composites to all pan base composites *)
ratio = Length[oddPanBase2500] / Length[panBase2500]
(* Print the first 50 pan base non-primes *)
Print["First 50 pan base non-primes:"]
Print[StringJoin[Riffle[ToString /@ Take[panBase2500, 50], ", "]]]
(* Print the first 20 odd pan base non-primes *)
Print["\nFirst 20 odd pan base non-primes:"]
Print[StringJoin[Riffle[ToString /@ Take[oddPanBase2500, 20], ", "]]]
(* Print the count of pan-base composites up to and including 2500 *)
Print["\nCount of pan-base composites up to and including 2500: ", Length[panBase2500]]
(* Print the ratios *)
Print["Odd up to and including 2500: ", Rationalize[ratio], ", or ", N[ratio * 100, 4], "%."]
Print["Even up to and including 2500: ", Rationalize[1 - ratio], ", or ", N[(1 - ratio) * 100, 4], "%."]</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 16.894018887722980063`4.%.
Even up to and including 2500: 792/953, or 83.105981112277019937`4.%.
</pre>
Line 671 ⟶ 815:
Percent odd up to and including 10000: 18.030657
Percent even up to and including 10000: 81.969343
</pre>
=={{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%.
</pre>
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