Multi-base primes: Difference between revisions

Content added Content deleted
m (→‎Up to base 62: make sub item)
m (→‎{{header|Pascal}}: using inc in base to speed up converting, CnvtoBase base was the true reason.)
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First counting the bases that convert a MAXBASE string of n into a prime number.<BR>
First counting the bases that convert a MAXBASE string of n into a prime number.<BR>
Afterwards only checking the maxcount for the used bases.<BR>
Afterwards only checking the maxcount for the used bases.<BR>
Most time consuming is sieving for the primes.
<lang pascal>program MAXBaseStringIsPrimeInBase;
<lang pascal>program MAXBaseStringIsPrimeInBase;
{$IFDEF FPC}
{$IFDEF FPC}
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sysutils;
sysutils;
const
const
CharOfBase= '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz';
MINBASE = 2;
MINBASE = 2;
MAXBASE = 36;//62;
MAXBASE = 62;//62;//36
MAXDIGITCOUNT = 6;//5;
MAXDIGITCOUNT = 5;//6;
type
type
tdigits = array [0..15] of byte;//must be 0..15
tdigits = record
dgtDgts : array [0..13] of byte;
dgtMaxIdx,
dgtMaxDgtVal :byte;
dgtNum : Uint64;
end;
tSol = array of Uint64;
tSol = array of Uint64;
var
var
BoolPrimes: array of boolean;
BoolPrimes: array of boolean;

//memorize the highest used digit
function Out_String(n:Uint64;var s: AnsiString):Uint32;forward;
MaxDgtPos : UInt32;

procedure Out_Digits(const dgts:tDigits);
var
s : ANsistring;
i : Int32;
begin
s := '';
with dgts do
Begin
i := dgtMaxIdx;
while i >= 0 do
begin
s := s+CharOfBase[dgtDgts[i]];
dec(i);
end;
end;
write(#13,s);
end;

function BuildWheel(primeLimit:Int64):NativeUint;
function BuildWheel(primeLimit:Int64):NativeUint;
var
var
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end;
end;


function getDgtsInMAXBASEandMaxDigit(n:Uint64;var dgt:tDigits):uint32;
procedure CnvtoMAXBASE(n:Uint64;var dgt:tDigits);
var
var
pQ :pQWord;
q,r: Uint64;
q,r: Uint64;
i:Int64;
i : Int32;
Begin
Begin
pQ := @dgt[0];
pQ[0] := 0;pQ[1] := 0;
//aka fillChar(dgt[0],SizeOf(dgt),#0);

i := 0;
i := 0;
result := 0;
with dgt do
repeat
Begin
q := n DIV MAXBASE;
dgtNum:= n;
repeat
r := (n-q*MAXBASE);
dgt[i] := r;
r := n;
if result < r then result := r;
q := n div MAXBASE;
inc(i);
r -= q*MAXBASE;
n := q;
n := q;
until n = 0;
dgtDgts[i] := r;
MaxDgtPos := i-1;
inc(i);
until (q = 0);
dec(i);
dgtMaxIdx := i;
r := 1;
repeat
q := dgtDgts[i];
if r < q then
r := q;
dec(i);
until i <0 ;
dgtMaxDgtVal := r;
end;
end;
end;


function CnvtoBase(const dgt:tDigits;base:NativeUint;DgtCnt:NativeInt):Uint64;
function CnvtoBase(const dgt:tDigits;base:NativeUint):Uint64;
var
tmpDgt,i: NativeInt;
Begin
Begin
result := 0;
result := 0;
with dgt do
repeat
Begin
result := base*result+dgt[DgtCnt];
dec(DgtCnt);
i:= dgtMaxIdx;
repeat
until (DgtCnt< 0);
//result := base*result + dgtDgts[i];
//this is th reason for speed up.Hide the waiting for reading of dgtDgts[i]
tmpDgt := dgtDgts[i];
result *= base;
dec(i);
result +=tmpDgt;
until (i< 0);
end;
end;
end;


procedure IncMAXBASEDigits(var dgt:tDigits);
function CntPrimeInBases(n:Uint64;max:Int32):Uint32;
var
i,q,tmp :NativeInt;
Begin
with dgt do
Begin
tmp := dgtMaxIdx;
i := 0;
repeat
q := dgtDgts[i]+1;
q -= (-ORD(q >=MAXBASE) AND MAXBASE);
dgtDgts[i] := q;
inc(i);
until q <> 0;
dec(i);
if tmp < i then
begin
tmp := i;
dgtMaxIdx := i;
end;

i := tmp;
repeat
tmp := dgtDgts[i];
if q< tmp then
q := tmp;
dec(i);
until i <0;
dgtMaxDgtVal := q;
end;
end;

function CntPrimeInBases(var Digits :tdigits;max:Int32):Uint32;
var
var
Digits :tdigits;
pr : Uint64;
pr : Uint64;
base,dgtCnt: Uint32;
base: Uint32;
begin
begin
result := 0;
result := 0;
Base := getDgtsInMAXBASEandMaxDigit(n,Digits)+1;
IncMAXBASEDigits(Digits);
Base := Digits.dgtMaxDgtVal+1;
IF Digits[0] = 0 then
//divisible by every base
IF Digits.dgtDgts[0] = 0 then
EXIT;
EXIT;
if base < MinBase then
base := MinBase;
// if (MAXBASE - Base) <= (max-result) then BREAK;
// if (MAXBASE - Base) <= (max-result) then BREAK;
max := (max+Base-MAXBASE);
max := (max+Base-MAXBASE);
if (max>=0) then
if (max>=0) then
EXIT;
EXIT;
for base := base TO MAXBASE do
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
begin
pr := CnvtoBase(Digits,base,MaxDgtPos);
pr := CnvtoBase(Digits,base);
inc(result,Ord(boolprimes[pr]));
inc(result,Ord(boolprimes[pr]));
//no chance to reach max then exit
//no chance to reach max then exit
if result<=max then
if result<max then
break;
break;
inc(max);
inc(max);
end;
end;
end;
end;


function GetMaxBaseCnt(MinLmt,MaxLmt:Uint32):tSol;
function GetMaxBaseCnt(var dgt:tDigits;MinLmt,MaxLmt:Uint32):tSol;
var
var
i : Uint32;
i : Uint32;
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For i := MinLmt to MaxLmt do
For i := MinLmt to MaxLmt do
Begin
Begin
baseCnt := CntPrimeInBases(i,max);
baseCnt := CntPrimeInBases(dgt,max);
if baseCnt = 0 then
if baseCnt = 0 then
continue;
continue;
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function Out_String(n:Uint64;var s: AnsiString):Uint32;
function Out_String(n:Uint64;var s: AnsiString):Uint32;
//out-sourced for debugging purpose
//out-sourced for debugging purpose
const
CharOfBase= '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz';
var
var
dgt:tDigits;
dgt:tDigits;
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Begin
Begin
result := 0;
result := 0;
base:= getDgtsInMAXBASEandMaxDigit(n,dgt)+1;
CnvtoMAXBASE(n,dgt);
sl := '';
sl := '';
with dgt do
i := MaxDgtPos;
begin
while (i>=0)do
base:= dgtMaxDgtVal+1;
Begin
sl += CharOfBase[dgt[i]+1];
i := dgtMaxIdx;
dec(i);
while (i>=0)do
Begin
sl += CharOfBase[dgtDgts[i]+1];
dec(i);
end;
s := sl+' -> [';
end;
end;
s := sl+' -> [';

For base := base to MAXBASE do
For base := base to MAXBASE do
if boolprimes[CnvtoBase(dgt,base,MaxDgtPos)] then
if boolprimes[CnvtoBase(dgt,base)] then
begin
begin
inc(result);
inc(result);
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var
var
dgt:tDigits;
T0 : Int64;
T0 : Int64;
i : NativeInt;
lmt,minLmt : UInt32;
lmt,minLmt : UInt32;

i : Uint32;
begin
begin
T0 := GetTickCount64;
T0 := GetTickCount64;
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for i := 1 to MAXDIGITCOUNT do
for i := 1 to MAXDIGITCOUNT do
lmt :=lmt*MAXBASE+MAXBASE-1;
lmt :=lmt*MAXBASE+MAXBASE-1;
writeln('max prime limit ',lmt);
writeln('max prime limit ',lmt);
Sieve(lmt);
Sieve(lmt);
writeln('Prime sieving ',(GetTickCount64-T0)/1000:6:3,' s');
writeln('Prime sieving ',(GetTickCount64-T0)/1000:6:3,' s');
CnvtoMAXBASE(0,dgt);
T0 := GetTickCount64;
T0 := GetTickCount64;
i := 1;
i := 1;
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repeat
repeat
write(i:2,' character strings which are prime in count bases = ');
write(i:2,' character strings which are prime in count bases = ');
Out_Sol(GetMaxBaseCnt(minLmt,MAXBASE*minLmt-1));
Out_Sol(GetMaxBaseCnt(dgt,minLmt,MAXBASE*minLmt-1));
minLmt *= MAXBASE;
minLmt *= MAXBASE;
inc(i);
inc(i);
until i>MAXDIGITCOUNT;
until i>MAXDIGITCOUNT;
writeln(' Converting ',(GetTickCount64-T0)/1000:6:3,' s');
writeln(' Converting ',(GetTickCount64-T0)/1000:6:3,' s');
{$IFDEF WINDOWS} readln; {$ENDIF}
{$IFDEF WINDOWS} readln; {$ENDIF}
end.</lang>
end.</lang>
{{out}}
{{out}}
<pre>
<pre>

//at home 2200G 16GB Linux
TIO.RUN// extreme volatile timings for sieving primes
max prime limit 916132831
Prime sieving 3.788 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 12.738 s
Real time: 16.768 s User time: 16.128 s Sys. time: 0.488 s CPU share: 99.09 %
//at home AMD 2200G Linux fpc 3.2.2
real 0m8,609s user 0m8,378s sys 0m0,220s
max prime limit 916132831
Prime sieving 1.734 s
Converting 6.842 s

//base = 36 maxcharacters = 6
//base = 36 maxcharacters = 6
max prime limit 2176782335
max prime limit 2176782335
Prime sieving 5.003 s
Prime sieving 4.986 s
1 character strings which are prime in count bases = 34
1 character strings which are prime in count bases = 34
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]
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]
Line 938: Line 1,040:
441431 -> [5,8,9,11,12,14,16,17,19,21,22,23,26,28,30,31,32,33]
441431 -> [5,8,9,11,12,14,16,17,19,21,22,23,26,28,30,31,32,33]


Converting 24.313 s
Converting 15.507 s// 24.3s before
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]


real 0m20,566s</pre>
Converting 19.044 s
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}}==
=={{header|Phix}}==
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