Strong and weak primes: Difference between revisions
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There are 37780 weak primes below 1,000,000
There are 321750 weak primes below 10,000,000</pre>
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
<syntaxhighlight lang="Delphi">
procedure StrongWeakPrimes(Memo: TMemo);
{Display Strong/Weak prime information}
var I,P: integer;
var Sieve: TPrimeSieve;
var S: string;
var Cnt,Cnt1,Cnt2: integer;
type TPrimeTypes = (ptStrong,ptWeak,ptBalanced);
function GetTypeStr(PrimeType: TPrimeTypes): string;
{Get string describing PrimeType}
begin
case PrimeType of
ptStrong: Result:='Strong';
ptWeak: Result:='Weak';
ptBalanced: Result:='Balanced';
end;
end;
function GetPrimeType(N: integer): TPrimeTypes;
{Return flag indicating type of prime Primes[N] is}
{Strong = Primes(N) > [Primes(N-1) + Primes(N+1)] / 2}
{Weak = Primes(N) < [Primes(N-1) + Primes(N+1)] / 2}
{Balanced = Primes(N) = [Primes(N-1) + Primes(N+1)] / 2}
var P,P1: double;
begin
P:=Sieve.Primes[N];
P1:=(Sieve.Primes[N-1] + Sieve.Primes[N+1]) / 2;
if P>P1 then Result:=ptStrong
else if P<P1 then Result:=ptWeak
else Result:=ptBalanced;
end;
procedure GetPrimeCounts(PT: TPrimeTypes; var Cnt1,Cnt2: integer);
{Get number of primes of type "PT" below 1 million and 10 million}
var I: integer;
begin
Cnt1:=0; Cnt2:=0;
for I:=1 to 1000000-1 do
begin
if GetPrimeType(I)=PT then
begin
if Sieve.Primes[I]>10000000 then break;
Inc(Cnt2);
if Sieve.Primes[I]<1000000 then Inc(Cnt1);
end;
end;
end;
function GetPrimeList(PT: TPrimeTypes; Limit: integer): string;
{Get a list of primes of type PT up to Limit}
var I,Cnt: integer;
begin
Result:='';
Cnt:=0;
for I:=1 to Sieve.PrimeCount-1 do
if GetPrimeType(I)=PT then
begin
Inc(Cnt);
P:=Sieve.Primes[I];
Result:=Result+Format('%5d',[P]);
if Cnt>=Limit then break;
if (Cnt mod 10)=0 then Result:=Result+CRLF;
end;
end;
procedure ShowPrimeTypeData(PT: TPrimeTypes; Limit: Integer);
{Display information about specified PrimeType, listing items up to Limit}
var S,TS: string;
begin
S:=GetPrimeList(PT,Limit);
TS:=GetTypeStr(PT);
Memo.Lines.Add(Format('First %d %s primes are:',[Limit,TS]));
Memo.Lines.Add(S);
GetPrimeCounts(PT,Cnt1,Cnt2);
Memo.Lines.Add(Format('Number %s primes <1,000,000: %8.0n', [TS,Cnt1+0.0]));
Memo.Lines.Add(Format('Number %s primes <10,000,000: %8.0n', [TS,Cnt2+0.0]));
Memo.Lines.Add('');
end;
begin
Sieve:=TPrimeSieve.Create;
try
Sieve.Intialize(200000000);
Memo.Lines.Add('Primes in Sieve : '+IntToStr(Sieve.PrimeCount));
ShowPrimeTypeData(ptStrong,36);
ShowPrimeTypeData(ptWeak,37);
ShowPrimeTypeData(ptBalanced,28);
finally Sieve.Free; end;
end;
</syntaxhighlight>
{{out}}
<pre>
Primes in Sieve : 11078937
First 36 Strong primes are:
11 17 29 37 41 59 67 71 79 97
101 107 127 137 149 163 179 191 197 223
227 239 251 269 277 281 307 311 331 347
367 379 397 419 431 439
Number Strong primes <1,000,000: 37,723
Number Strong primes <10,000,000: 320,991
First 37 Weak primes are:
3 7 13 19 23 31 43 47 61 73
83 89 103 109 113 131 139 151 167 181
193 199 229 233 241 271 283 293 313 317
337 349 353 359 383 389 401
Number Weak primes <1,000,000: 37,780
Number Weak primes <10,000,000: 321,750
First 28 Balanced primes are:
5 53 157 173 211 257 263 373 563 593
607 653 733 947 977 1103 1123 1187 1223 1367
1511 1747 1753 1907 2287 2417 2677 2903
Number Balanced primes <1,000,000: 2,994
Number Balanced primes <10,000,000: 21,837
Elapsed Time: 2.947 Sec.
</pre>
=={{header|Factor}}==
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