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Multi-base primes: Difference between revisions
→{{header|Pascal}}: extended like raku and phix to base 62
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(→{{header|Pascal}}: extended like raku and phix to base 62) |
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=={{header|Pascal}}==
First counting the bases that convert a
Afterwards only checking the maxcount for the used bases.<BR>
Most time consuming is sieving for the primes.
<lang pascal>program
{$IFDEF FPC}
{$MODE DELPHI}
{$OPTIMIZATION ON,ALL}
{$ELSE}
{$APPTYPE CONSOLE}
Line 559 ⟶ 558:
const
MINBASE = 2;
MAXBASE = 36;//
MAXDIGITCOUNT = 6;//
type
tdigits = array [0..15] of byte;//must be 0..15
tSol = array of
var
BoolPrimes: array of boolean;
//memorize the highest used digit
MaxDgtPos : UInt32;
function BuildWheel(primeLimit:Int64):NativeUint;
var
myPrimes : pBoolean;
Line 616 ⟶ 614:
end;
until WheelSize >= PrimeLimit;
while wpno > 0 do
begin
Line 626 ⟶ 624:
BuildWheel := pr+1;
end;
procedure Sieve(PrimeLimit:
var
myPrimes : pBoolean;
Line 655 ⟶ 653:
end;
function
var
pQ :pQWord;
q,r
i:Int64;
Begin
pQ := @dgt[0]
pQ[0] := 0;pQ[1] := 0;
//aka fillChar(dgt[0],SizeOf(dgt),#0);
i := 0;
result := 0;
repeat
q := n DIV
r := (n-q*
dgt[i] := r;
if result < r then result := r;
inc(i);
until n = 0;
MaxDgtPos := i-1;
end;
function CnvtoBase(const dgt:tDigits;base:
Begin
result := 0;
repeat
result := base*result+dgt[
dec(
until (
end;
function CntPrimeInBases(n:
var
Digits :tdigits;
base,dgtCnt: Uint32;
begin
Base := getDgtsInMAXBASEandMaxDigit(n,Digits)+1;
IF Digits[0] = 0 then
EXIT;
if base < MinBase then
base := MinBase;
// if (MAXBASE - Base) <= (max-result) then BREAK;
max := (max+Base-MAXBASE);
if (max>=0) then
EXIT;
dgtCnt := MAXDIGITCOUNT-1;
while (dgtCnt>0) AND (Digits[dgtCnt]= 0) do
dec(dgtCnt);
result := Ord(boolprimes[n]);
for base := base TO MAXBASE-1 do
begin
pr := CnvtoBase(Digits,base,MaxDgtPos);
inc(result,Ord(boolprimes[pr]));
//no chance to reach max then exit
if result<=max then
break;
inc(max);
end;
end;
function GetMaxBaseCnt(MinLmt,MaxLmt:Uint32):tSol;
var
i
baseCnt,max,Idx: Int32;
Begin
setlength(result,0);
Line 718 ⟶ 726:
For i := MinLmt to MaxLmt do
Begin
baseCnt := CntPrimeInBases(i,max);
if baseCnt = 0 then
continue;
Line 741 ⟶ 749:
end;
function Out_String(n:
//out-sourced for debugging purpose
const
CharOfBase= '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz';
var
dgt:tDigits;
sl : string[8];
base,
Begin
result := 0;
base:= getDgtsInMAXBASEandMaxDigit(n,dgt)+1;
sl := '';
i := MaxDgtPos;
while (i>=0)do
Begin
sl += CharOfBase[dgt[i]+1];
dec(i);
end;
s := sl+' -> [';
For base :=
if boolprimes[CnvtoBase(dgt,base,MaxDgtPos)] then
begin
inc(result);
Line 782 ⟶ 799:
var
T0 : Int64;
i : Uint32;
begin
T0 := GetTickCount64;
lmt := 0;
//maxvalue
for i := 1 to MAXDIGITCOUNT do
lmt :=
writeln('max prime limit ',lmt);
Sieve(lmt);
Line 797 ⟶ 815:
repeat
write(i:2,' character strings which are prime in count bases = ');
Out_Sol(GetMaxBaseCnt(minLmt,
minLmt *=
inc(i);
until
writeln(' Converting ',(GetTickCount64-T0)/1000:6:3,' s');
{$IFDEF WINDOWS} readln; {$ENDIF}
Line 806 ⟶ 824:
{{out}}
<pre>
//at home 2200G 16GB Linux
//base = 36 maxcharacters = 6
max prime limit 2176782335
Prime sieving 5.003 s
1 character strings which are prime in count bases = 34
2 character strings which are prime in count bases = 18
3 character strings which are prime in count bases = 18
4 character strings which are prime in count bases = 19
5 character strings which are prime in count bases = 18
6 character strings which are prime in count bases = 18
Converting 24.313 s
real 0m29,389s
######################
TIO.RUN// extreme volatile timings for sieving primes
Maxbase = 62 maxcharacters = 5
max prime limit 916132831
Prime sieving 14.576 s
1 character strings which are prime in count bases = 60
2 -> [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62]
2 character strings which are prime in count bases = 31
65 -> [7,8,9,11,13,14,16,17,18,21,22,24,27,28,29,31,32,37,38,39,41,42,43,44,46,48,51,52,57,58,59]
3 character strings which are prime in count bases = 33
1L1 -> [22,23,25,26,27,28,29,30,31,32,33,34,36,38,39,40,41,42,43,44,45,46,48,51,52,53,54,57,58,59,60,61,62]
B9B -> [13,14,15,16,17,19,20,21,23,24,26,27,28,30,31,34,36,39,40,42,45,47,49,50,52,53,54,57,58,59,60,61,62]
4 character strings which are prime in count bases = 32
1727 -> [8,9,11,12,13,15,16,17,19,20,22,23,24,26,27,29,31,33,36,37,38,39,41,45,46,48,50,51,57,58,60,61]
417B -> [12,13,15,16,17,18,19,21,23,25,28,30,32,34,35,37,38,39,41,45,48,49,50,51,52,54,56,57,58,59,61,62]
5 character strings which are prime in count bases = 30
50161 -> [7,8,9,13,17,18,19,20,25,28,29,30,31,33,35,36,38,39,41,42,43,44,47,48,52,55,56,59,60,62]
Converting
Real time: 33.929 s User time: 24.091 s Sys. time: 9.093 s CPU share: 97.80 %
//at home real 0m12,614s user 0m12,336s sys 0m0,238s
</pre>
=={{header|Phix}}==
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