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# question

Joe keane
Guest
Posts: n/a

 01-12-2012
What is the greatest set of four primes ssuch that they ae all <2^64?

Joe Pfeiffer
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Posts: n/a

 01-12-2012
http://www.velocityreviews.com/forums/(E-Mail Removed) (Joe keane) writes:

> What is the greatest set of four primes ssuch that they ae all <2^64?

Hmm, I'll bet you could write a C program to solve that homework
question....

Tim Little
Guest
Posts: n/a

 01-12-2012
On 2012-01-12, Joe keane <(E-Mail Removed)> wrote:
> What is the greatest set of four primes ssuch that they ae all <2^64?

Assuming some reasonable meaning for "greatest set",
{18446744073709551557, 18446744073709551533, 18446744073709551521,
18446744073709551437}.

Is there some significance to the question?

--
Tim

Kaz Kylheku
Guest
Posts: n/a

 01-12-2012
On 2012-01-12, Joe keane <(E-Mail Removed)> wrote:
> What is the greatest set of four primes ssuch that they ae all <2^64?

You mean, in the ordered list of primes below 2^64, what are the four highest
entries?

88888 Dihedral
Guest
Posts: n/a

 01-12-2012
x=2^64 -a for a not to be even and a%3 !=1 and maybe some other restrictions first, then the AKS primality test or Miller-rabin primality test can be applied.

Since the type unsigned long long is available in 64 bit GCC, so GMP library
may not be required at this case.

I

Dann Corbit
Guest
Posts: n/a

 01-12-2012
In article <(E-Mail Removed)>, (E-Mail Removed) says...
>
> On 2012-01-12, Joe keane <(E-Mail Removed)> wrote:
> > What is the greatest set of four primes ssuch that they ae all <2^64?

>
> You mean, in the ordered list of primes below 2^64, what are the four highest
> entries?

If so, it would have been better to phrase it as:
"What are the 4 largest primes less than 2^64?"

If that is the original question, then the answer is very simple:

Apply a primality test to odd numbers starting at 2^64th-1 and work
backwards until you find 4 of them.

Even doing it by hand would take less than a few minutes, I am sure.
Faster than writing a program, at least.

Actually, I used a batch file:

c:\tmp>Factor 18446744073709551615
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 5
PRIME FACTOR 17
PRIME FACTOR 257
PRIME FACTOR 641
now trying 1000 iterations of brent's method
iterations= 0 10 20PRIME FACTOR 65537
PRIME FACTOR 6700417

c:\tmp>Factor 18446744073709551613
first trying brute force division by small primes
PRIME FACTOR 13
PRIME FACTOR 3889
PRIME FACTOR 364870227143809

c:\tmp>Factor 18446744073709551611
first trying brute force division by small primes
PRIME FACTOR 11
PRIME FACTOR 59
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200 210 220 230 240 250
260 270 280 290 300 310 320 330 340 350 360 370 380 390
400 410 420 430 440 450 460 470 480 490 500 510 520 530
540 550 560 570 580 590 600 610 620 630 640 650 660 670
680 690 700 710 720 730 740 750 760 770 780 790 800 810
820 830 840 850 860 870 880 890 900 910 920 930 940 950
960 970 980 990 1000finally - the multiple polynomial quadratic sieve
- with large prime (*)
using multiplier k= 11 and 25 small primes as factor base
working 0 1 2 3 4 5 6 7 8 9*
10 11 12 13 14 15 16 17 18
trying
PRIME FACTOR 98818999
PRIME FACTOR 287630261

c:\tmp>Factor 18446744073709551609
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 3
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200 210 220 230 240 250
260 270 280 290 300 310 320 330 340 350 360 370 380 390
400 410 420 430 440 450 460 470 480 490 500 510 520 530
540 550 560 570 580 590 600 610 620 630 640 650 660 670
680 690 700 710 720 730 740 750 760 770 780 790 800 810
820 830 840 850 860 870 880 890 900 910 920 930 940 950
960 970 980 990 1000finally - the multiple polynomial quadratic sieve
- with large prime (*)
using multiplier k= 1 and 25 small primes as factor base
working 0 1 2* 3 4 5 6* 7 8 9
10 11 12 13 14 15 16 17* 18 19 20 21*
22* 23
trying
working 23 24 25
trying
PRIME FACTOR 818923289
PRIME FACTOR 2502845209

c:\tmp>Factor 18446744073709551607
first trying brute force division by small primes
PRIME FACTOR 7
PRIME FACTOR 9241
now trying 1000 iterations of brent's method
iterations= 0 10 20PRIME FACTOR 464773
PRIME FACTOR 613566757

c:\tmp>Factor 18446744073709551605
first trying brute force division by small primes
PRIME FACTOR 5
PRIME FACTOR 2551
PRIME FACTOR 1446236305269271

c:\tmp>Factor 18446744073709551603
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 139
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50PRIME FACTOR 2306123
PRIME FACTOR 19182323033

c:\tmp>Factor 18446744073709551601
first trying brute force division by small primes
PRIME FACTOR 53
PRIME FACTOR 348051774975651917

c:\tmp>Factor 18446744073709551599
first trying brute force division by small primes
PRIME FACTOR 19
PRIME FACTOR 67
PRIME FACTOR 14490765179661863

c:\tmp>Factor 18446744073709551597
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 6148914691236517199

c:\tmp>Factor 18446744073709551595
first trying brute force division by small primes
PRIME FACTOR 5
PRIME FACTOR 373
PRIME FACTOR 3301
PRIME FACTOR 2996369460503

c:\tmp>Factor 18446744073709551593
first trying brute force division by small primes
PRIME FACTOR 7
now trying 1000 iterations of brent's method
iterations= 0 10PRIME FACTOR 16547
PRIME FACTOR 159258424692517

c:\tmp>Factor 18446744073709551591
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 3
PRIME FACTOR 3
PRIME FACTOR 47
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200PRIME FACTOR 3384529
PRIME FACTOR 4294967291

c:\tmp>Factor 18446744073709551589
first trying brute force division by small primes
PRIME FACTOR 11
PRIME FACTOR 13177
PRIME FACTOR 127265442359687

c:\tmp>Factor 18446744073709551587
first trying brute force division by small primes
PRIME FACTOR 13
PRIME FACTOR 23
PRIME FACTOR 23
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200 210 220 230 240PRIME
FACTOR 16561661
PRIME FACTOR 161963371

c:\tmp>Factor 18446744073709551585
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 5
PRIME FACTOR 499
PRIME FACTOR 2593
PRIME FACTOR 950441521877

c:\tmp>Factor 18446744073709551583
first trying brute force division by small primes
PRIME FACTOR 827
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50 60 70PRIME FACTOR
3894899
PRIME FACTOR 5726879071

c:\tmp>Factor 18446744073709551581
first trying brute force division by small primes
PRIME FACTOR 17
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200 210 220 230 240 250
260 270 280 290 300 310 320 330 340 350 360 370 380 390
400 410 420 430 440 450 460 470 480 490 500 510PRIME FACTOR
72786899
PRIME FACTOR 14907938207

c:\tmp>Factor 18446744073709551579
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 7
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200 210 220 230 240 250
260 270 280 290 300 310 320 330 340 350 360 370 380 390
400 410 420 430 440 450 460 470 480 490 500 510 520PRIME
FACTOR 57906439
PRIME FACTOR 15169580441

c:\tmp>Factor 18446744073709551577
first trying brute force division by small primes
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200 210 220 230 240 250
260 270 280 290 300 310 320 330 340 350 360 370 380 390
400 410 420 430 440PRIME FACTOR 139646831
PRIME FACTOR 132095686967

c:\tmp>Factor 18446744073709551575
first trying brute force division by small primes
PRIME FACTOR 5
PRIME FACTOR 5
PRIME FACTOR 43
now trying 1000 iterations of brent's method
iterations= 0 10 20 30PRIME FACTOR 122099
PRIME FACTOR 140539741759

c:\tmp>Factor 18446744073709551573
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 3
now trying 1000 iterations of brent's method
iterations= 0 10PRIME FACTOR 31799
PRIME FACTOR 64456059323003

c:\tmp>Factor 18446744073709551571
first trying brute force division by small primes
PRIME FACTOR 11071
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50PRIME FACTOR 844709
PRIME FACTOR 1972539689

c:\tmp>Factor 18446744073709551569
first trying brute force division by small primes
PRIME FACTOR 31
PRIME FACTOR 173
PRIME FACTOR 9419
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40PRIME FACTOR 439771
PRIME FACTOR 830387

c:\tmp>Factor 18446744073709551567
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 11
PRIME FACTOR 37
PRIME FACTOR 167
PRIME FACTOR 223
PRIME FACTOR 1039
PRIME FACTOR 6323
PRIME FACTOR 61751

c:\tmp>Factor 18446744073709551565
first trying brute force division by small primes
PRIME FACTOR 5
PRIME FACTOR 7
PRIME FACTOR 7
PRIME FACTOR 79
PRIME FACTOR 599
PRIME FACTOR 659
PRIME FACTOR 2414428283

c:\tmp>Factor 18446744073709551563
first trying brute force division by small primes
PRIME FACTOR 29
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200 210 220 230 240 250
260 270 280 290 300 310 320 330 340 350 360 370 380 390
400 410 420 430 440 450 460 470 480 490 500 510 520 530
540 550 560 570 580 590 600 610 620 630 640 650 660 670
680 690 700 710 720 730 740 750 760 770 780 790 800 810
820 830 840 850 860 870 880 890 900 910 920 930 940 950
960 970 980 990 1000finally - the multiple polynomial quadratic sieve
- with large prime (*)
using multiplier k= 7 and 25 small primes as factor base
working 0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16* 17 18 19* 20 21
22 23 24
trying
PRIME FACTOR 74187931
PRIME FACTOR 8574098437

c:\tmp>Factor 18446744073709551561
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 13
PRIME FACTOR 19
PRIME FACTOR 103
PRIME FACTOR 1811
PRIME FACTOR 133458377137

c:\tmp>Factor 18446744073709551559
first trying brute force division by small primes
PRIME FACTOR 41
PRIME FACTOR 163
PRIME FACTOR 269
PRIME FACTOR 8807
PRIME FACTOR 1165112831

c:\tmp>Factor 18446744073709551557
this number is prime!

c:\tmp>Factor 18446744073709551555
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 3
PRIME FACTOR 5
PRIME FACTOR 97
PRIME FACTOR 197
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40PRIME FACTOR 325957
PRIME FACTOR 65812583

c:\tmp>Factor 18446744073709551553
first trying brute force division by small primes
PRIME FACTOR 401
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200 210 220 230 240 250
260 270 280 290 300 310 320 330 340 350 360 370 380 390
400 410 420 430PRIME FACTOR 385788209
PRIME FACTOR 119241217

c:\tmp>Factor 18446744073709551551
first trying brute force division by small primes
PRIME FACTOR 7
PRIME FACTOR 131
PRIME FACTOR 20116405751046403

c:\tmp>Factor 18446744073709551549
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 89
PRIME FACTOR 69088929115017047

c:\tmp>Factor 18446744073709551547
first trying brute force division by small primes
PRIME FACTOR 17
PRIME FACTOR 211
PRIME FACTOR 251
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50 60 70 80 90 100 110
120 130PRIME FACTOR 1101431
PRIME FACTOR 18601901

c:\tmp>Factor 18446744073709551545
first trying brute force division by small primes
PRIME FACTOR 5
PRIME FACTOR 11
PRIME FACTOR 3319
now trying 1000 iterations of brent's method
iterations= 0 10 20PRIME FACTOR 36871
PRIME FACTOR 2740721231

c:\tmp>Factor 18446744073709551543
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 839
PRIME FACTOR 7328861372153179

c:\tmp>Factor 18446744073709551541
first trying brute force division by small primes
PRIME FACTOR 23
PRIME FACTOR 73
PRIME FACTOR 7283
PRIME FACTOR 1508546551513

c:\tmp>Factor 18446744073709551539
first trying brute force division by small primes
PRIME FACTOR 61
now trying 1000 iterations of brent's method
iterations= 0 10 20 30PRIME FACTOR 268909
PRIME FACTOR 1124564966411

c:\tmp>Factor 18446744073709551537
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 3
PRIME FACTOR 3
PRIME FACTOR 7
PRIME FACTOR 101
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200 210 220 230 240 250
260 270 280 290 300 310 320 330 340 350 360 370 380PRIME
FACTOR 126753007
PRIME FACTOR 7623919

c:\tmp>Factor 18446744073709551535
first trying brute force division by small primes
PRIME FACTOR 5
PRIME FACTOR 13
PRIME FACTOR 71
PRIME FACTOR 71
PRIME FACTOR 9629
now trying 1000 iterations of brent's method
iterations= 0 10PRIME FACTOR 89209
PRIME FACTOR 65539

c:\tmp>Factor 18446744073709551533
this number is prime!

c:\tmp>Factor 18446744073709551531
first trying brute force division by small primes
PRIME FACTOR 3
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200 210 220 230 240 250
260 270 280 290 300 310 320 330 340 350 360 370 380 390
400 410 420 430 440 450 460 470 480 490 500 510 520 530
540 550 560 570 580 590 600 610 620 630 640 650 660 670
680 690 700 710 720PRIME FACTOR 962165251
PRIME FACTOR 6390705427

c:\tmp>Factor 18446744073709551529
first trying brute force division by small primes
PRIME FACTOR 14843
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200 210 220 230 240 250
260 270 280 290 300 310 320 330 340 350 360 370 380 390
400 410 420 430 440 450 460 470 480 490 500 510 520 530
540 550 560 570 580PRIME FACTOR 13973891
PRIME FACTOR 88936633

c:\tmp>Factor 18446744073709551527
first trying brute force division by small primes
now trying 1000 iterations of brent's method
iterations= 0 10 20PRIME FACTOR 17099
PRIME FACTOR 1078820052266773

c:\tmp>Factor 18446744073709551525
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 5
PRIME FACTOR 5
PRIME FACTOR 4441
PRIME FACTOR 55383154165607

c:\tmp>Factor 18446744073709551523
first trying brute force division by small primes
PRIME FACTOR 7
PRIME FACTOR 11
PRIME FACTOR 11
PRIME FACTOR 19
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50PRIME FACTOR 6897409
PRIME FACTOR 166186879

c:\tmp>Factor 18446744073709551521
this number is prime!

c:\tmp>Factor 18446744073709551519
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 3
PRIME FACTOR 307
now trying 1000 iterations of brent's method
iterations= 0 10PRIME FACTOR 405029
PRIME FACTOR 16483624697

c:\tmp>Factor 18446744073709551517
first trying brute force division by small primes
PRIME FACTOR 397
PRIME FACTOR 46465350311610961

c:\tmp>Factor 18446744073709551515
first trying brute force division by small primes
PRIME FACTOR 5
PRIME FACTOR 281
PRIME FACTOR 13129355212604663

c:\tmp>Factor 18446744073709551513
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 17
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50 60 70 80 90PRIME
FACTOR 3427981
PRIME FACTOR 105514255823

c:\tmp>Factor 18446744073709551511
first trying brute force division by small primes
PRIME FACTOR 2617
PRIME FACTOR 7048813172987983

c:\tmp>Factor 18446744073709551509
first trying brute force division by small primes
PRIME FACTOR 7
PRIME FACTOR 13
PRIME FACTOR 202711473337467599

c:\tmp>Factor 18446744073709551507
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 31
PRIME FACTOR 293
PRIME FACTOR 676969579570243

c:\tmp>Factor 18446744073709551505
first trying brute force division by small primes
PRIME FACTOR 5
PRIME FACTOR 29
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50 60PRIME FACTOR 160649
PRIME FACTOR 791906109881

c:\tmp>Factor 18446744073709551503
first trying brute force division by small primes
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200 210 220PRIME FACTOR
119026343
PRIME FACTOR 154980348121

c:\tmp>Factor 18446744073709551501
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 3
PRIME FACTOR 11
PRIME FACTOR 186330748219288399

c:\tmp>Factor 18446744073709551499
first trying brute force division by small primes
now trying 1000 iterations of brent's method
iterations= 0 10 20 30PRIME FACTOR 363269
PRIME FACTOR 50779846542671

c:\tmp>Factor 18446744073709551497
first trying brute force division by small primes
PRIME FACTOR 47
PRIME FACTOR 83
PRIME FACTOR 4728721885083197

c:\tmp>Factor 18446744073709551495
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 5
PRIME FACTOR 7
PRIME FACTOR 23
PRIME FACTOR 53
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50 60 70PRIME FACTOR
1174451
PRIME FACTOR 122713351

c:\tmp>Factor 18446744073709551493
first trying brute force division by small primes
PRIME FACTOR 37
PRIME FACTOR 59
PRIME FACTOR 8221
PRIME FACTOR 1027877450351

c:\tmp>Factor 18446744073709551491
first trying brute force division by small primes
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50 60 70 80 90 100 110
120 130PRIME FACTOR 315781601
PRIME FACTOR 58416145891

c:\tmp>Factor 18446744073709551489
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 43
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150PRIME FACTOR 2855443
PRIME FACTOR 50079100187

c:\tmp>Factor 18446744073709551487
first trying brute force division by small primes
PRIME FACTOR 127
PRIME FACTOR 145249953336295681

c:\tmp>Factor 18446744073709551485
first trying brute force division by small primes
PRIME FACTOR 5
PRIME FACTOR 19
now trying 1000 iterations of brent's method
iterations= 0 10PRIME FACTOR 159701
PRIME FACTOR 1215873747863

c:\tmp>Factor 18446744073709551483
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 3
PRIME FACTOR 3
PRIME FACTOR 3
PRIME FACTOR 3
PRIME FACTOR 13
PRIME FACTOR 2221
PRIME FACTOR 2629187374097

c:\tmp>Factor 18446744073709551481
first trying brute force division by small primes
PRIME FACTOR 7
PRIME FACTOR 3851
PRIME FACTOR 684302558656733

c:\tmp>Factor 18446744073709551479
first trying brute force division by small primes
PRIME FACTOR 11
PRIME FACTOR 17
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50PRIME FACTOR 13472579
PRIME FACTOR 7321960423

c:\tmp>Factor 18446744073709551477
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 41
PRIME FACTOR 941
PRIME FACTOR 159376757762539

c:\tmp>Factor 18446744073709551475
first trying brute force division by small primes
PRIME FACTOR 5
PRIME FACTOR 5
PRIME FACTOR 523
PRIME FACTOR 701
PRIME FACTOR 2012611764533

c:\tmp>Factor 18446744073709551473
first trying brute force division by small primes
PRIME FACTOR 113
PRIME FACTOR 383
PRIME FACTOR 521
now trying 1000 iterations of brent's method
iterations= 0 10 20 30PRIME FACTOR 260191
PRIME FACTOR 3144217

c:\tmp>Factor 18446744073709551471
first trying brute force division by small primes
PRIME FACTOR 3
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50PRIME FACTOR 7144591
PRIME FACTOR 860639145227

c:\tmp>Factor 18446744073709551469
first trying brute force division by small primes
now trying 1000 iterations of brent's method
iterations= 0 10PRIME FACTOR 52561
iterations= 19 20 30 40 50 60 70 80 90 100 110 120
130 140 150 160 170 180 190 200 210 220 230 240 250 260
270 280 290 300 310 320 330 340 350 360 370 380 390 400
410 420PRIME FACTOR 41590091
PRIME FACTOR 8438519

c:\tmp>Factor 18446744073709551467
first trying brute force division by small primes
PRIME FACTOR 7
PRIME FACTOR 7
PRIME FACTOR 719
PRIME FACTOR 523594109554357

c:\tmp>Factor 18446744073709551465
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 3
PRIME FACTOR 5
PRIME FACTOR 67
PRIME FACTOR 6118323075857231

c:\tmp>Factor 18446744073709551463
first trying brute force division by small primes
PRIME FACTOR 14879
PRIME FACTOR 1239783861395897

c:\tmp>Factor 18446744073709551461
first trying brute force division by small primes
now trying 1000 iterations of brent's method
iterations= 0 10PRIME FACTOR 76511
PRIME FACTOR 241099241595451

c:\tmp>Factor 18446744073709551459
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 601
PRIME FACTOR 6473
PRIME FACTOR 1580586938561

c:\tmp>Factor 18446744073709551457
first trying brute force division by small primes
PRIME FACTOR 11
PRIME FACTOR 13
PRIME FACTOR 128998210305661199

c:\tmp>Factor 18446744073709551455
first trying brute force division by small primes
PRIME FACTOR 5
PRIME FACTOR 9041
PRIME FACTOR 408068666601251

c:\tmp>Factor 18446744073709551453
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 7
PRIME FACTOR 878416384462359593

c:\tmp>Factor 18446744073709551451
first trying brute force division by small primes
PRIME FACTOR 1291
PRIME FACTOR 14288725076459761

c:\tmp>Factor 18446744073709551449
first trying brute force division by small primes
PRIME FACTOR 23
PRIME FACTOR 151
PRIME FACTOR 347
PRIME FACTOR 15306837243179

c:\tmp>Factor 18446744073709551447
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 3
PRIME FACTOR 19
PRIME FACTOR 29
PRIME FACTOR 389
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200 210 220PRIME FACTOR
1226783
PRIME FACTOR 7794859

c:\tmp>Factor 18446744073709551445
first trying brute force division by small primes
PRIME FACTOR 5
PRIME FACTOR 17
PRIME FACTOR 31
PRIME FACTOR 157
PRIME FACTOR 683
PRIME FACTOR 65285802497

c:\tmp>Factor 18446744073709551443
first trying brute force division by small primes
now trying 1000 iterations of brent's method
iterations= 0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200 210 220 230 240 250
260 270 280 290 300 310 320 330 340 350 360 370 380 390
400 410 420 430 440 450 460 470 480 490 500 510 520 530
540 550 560 570 580 590 600 610 620 630 640 650 660 670
680 690 700 710 720 730 740 750 760 770 780 790 800 810
820 830 840 850 860 870 880 890 900 910 920 930 940 950
960 970 980 990 1000finally - the multiple polynomial quadratic sieve
- with large prime (*)
using multiplier k= 2 and 25 small primes as factor base
working 0 1 2 3 4 5 6 7 8 9
10* 11* 12 13 14 15 16 17 18 19 20 21*
trying
working 21 22
trying
working 22 23 24
trying
PRIME FACTOR 3183958073
PRIME FACTOR 5793651691

c:\tmp>Factor 18446744073709551441
first trying brute force division by small primes
PRIME FACTOR 3
PRIME FACTOR 109
PRIME FACTOR 277
PRIME FACTOR 1801
PRIME FACTOR 113078096179

c:\tmp>Factor 18446744073709551439
first trying brute force division by small primes
PRIME FACTOR 7
PRIME FACTOR 2635249153387078777

c:\tmp>Factor 18446744073709551437
this number is prime!

So we have this then:
{18446744073709551557, 18446744073709551533, 18446744073709551521,
18446744073709551437}

I'm not going to pretend that there is any hope to find a C question in
here.

The Last Danish Pastry
Guest
Posts: n/a

 01-12-2012
"Joe keane" <(E-Mail Removed)> wrote...

> What is the greatest set of four primes ssuch that they ae all <2^64?

"question" is an unsatisfactory Subject line for a thread here.

Type

solve(a=2^64;b=previous prime(a);c=previous prime(b);d=previous
prime(c);e=previous prime(d))

into Wolfram Alpha
http://www.wolframalpha.com/

--
Clive Tooth

The Last Danish Pastry
Guest
Posts: n/a

 01-12-2012
"The Last Danish Pastry" <(E-Mail Removed)> wrote...

> "Joe keane" <(E-Mail Removed)> wrote...
>
>> What is the greatest set of four primes ssuch that they ae all <2^64?

>
> "question" is an unsatisfactory Subject line for a thread here.
>
> Type
>
> solve(a=2^64;b=previous prime(a);c=previous prime(b);d=previous
> prime(c);e=previous prime(d))
>
> into Wolfram Alpha
> http://www.wolframalpha.com/

Then try typing this in...

solve(h-1=previous prime(h))

--
Clive Tooth

88888 Dihedral
Guest
Posts: n/a

 01-13-2012
To factor an arbitrary long integer is harder than the primality check of a
long integer. Of course if one can factor the integers in the specified range,
then one solves the both problems.