Blum integer: Difference between revisions
Added better XPL0 example.
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(Added better XPL0 example.) |
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The 26828th Blum integer is: 524273
</pre>
Faster factoring. Does stretch. Takes 9.2 seconds.
<syntaxhighlight lang "XPL0">include xpllib; \for Print
int Prime1;
func Semiprime(N); \Returns 'true' if odd N is semiprime
int N, D, C;
[C:= 0; D:= 3;
while D*D <= N do
[while rem(N/D) = 0 do
[if C = 2 then return false;
C:= C+1;
N:= N/D;
];
D:= D+2;
];
Prime1:= N;
return C = 1;
];
int N, C, I, Goal, Prime2;
int FD, DC(10); \final digit and digit counters
[Text(0, "First 50 Blum integers:^m^j");
N:= 3; C:= 0; Goal:= 100_000;
for I:= 0 to 9 do DC(I):= 0;
loop [if Semiprime(N) then
[if rem(Prime1/4) = 3 then
[Prime2:= N/Prime1;
if rem(Prime2/4) = 3 and Prime2 # Prime1 then
[C:= C+1;
if C <= 50 then
[Print("%5d", N);
if rem(C/10) = 0 then Print("\n");
];
if C = 26_828 then
Print("\nThe 26,828th Blum integer is: %7,d\n", N);
if C = Goal then
[Print("The %6,dth Blum integer is: %7,d\n", Goal, N);
if Goal = 400_000 then quit;
Goal:= Goal + 100_000;
];
FD:= rem(N/10);
DC(FD):= DC(FD)+1;
];
];
];
N:= N+2;
];
Print("\n% distribution of the first 400,000 Blum integers:\n");
for I:= 0 to 9 do
if DC(I) > 0 then
Print("%4.3f\% end in %d\n", float(DC(I)) / 4_000., I);
]</syntaxhighlight>
{{out}}
<pre>
First 50 Blum integers:
21 33 57 69 77 93 129 133 141 161
177 201 209 213 217 237 249 253 301 309
321 329 341 381 393 413 417 437 453 469
473 489 497 501 517 537 553 573 581 589
597 633 649 669 681 713 717 721 737 749
The 26,828th Blum integer is: 524,273
The 100,000th Blum integer is: 2,075,217
The 200,000th Blum integer is: 4,275,533
The 300,000th Blum integer is: 6,521,629
The 400,000th Blum integer is: 8,802,377
% distribution of the first 400,000 Blum integers:
25.001% end in 1
25.017% end in 3
24.997% end in 7
24.985% end in 9
</pre>
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