Mersenne primes, 2^6mill.-1. [LONG 26k].

rem  >  pgms.programspd.maths.M6006e3,

factor Mersenne numbers, M_p = 2^6million-1.
world's largest known prime number May-July 1999 =
	 2^ 6.97(+)million -1.
greater than 2 million decimal digits. [Clarkson?]

web site
GIMPS - great internet mersenne prime search.

date:  05.09.99  21:30  pm.  nzst
don mcdonald**  Wellington New Zealand.
to: Nick Craig-Wood. **Numbers Module
ng: comp.sys.acorn.apps.

Nick -  greeting,
I've used your programs.
Thanks very much.
1000 decimals of Pi, etc.

Your calculator instantly verifies several of the following
results.

enter base [retn 2], a = ?
   reduced printout/  index  6003000
  =  2

powmod (infinite? precision ) function
powmod(a,b,c) = (a^b) MOD c.

maths.powrabc1 :
          PRINT  '; "k = ";(p-1)/n  " . LOG = ";INT(10*LOG p)", ";
          p " divides  ";a "^ "; n " -1 .. csec = "TIME-NOW
$.moddata :
  k = 6 . LOG = 75, 36018007 divides  2^ 6003001 -1 .. centisec = 33

if q is a divisor of a^prime - 1	[raised to the power of]
then q necessarily is of the form q= 2k*prime +1.

E.g. 6*6003001 +1 =  3601 8007.
(not sure, see book on number theory.)

check..  A = 6003001
powmod(2,A,6*A+1)  ==  1.

	between 10^7, 10^9.
	finds factor up to approx. 180million
	or else loss of precision.

regards  //  don.

  k = 6 . LOG = 7.5, 36018679 divides  2^ 6003113 -1 .. csec = 33
  k = 30 . LOG = .82, 180099391 divides  2^ 6003313 -1 .. csec = 132
  k = 2 . LOG = 7.0, 12006887 divides  2^ 6003443 -1 .. csec = 17
  k = 22 . LOG = .81, 132080279 divides  2^ 6003649 -1 .. csec = 99
  k = 8 . LOG = 7.6**, 48029273 divides  2^ 6003659 -1 .. csec = 43
  k = 2 . LOG = 7.0**, 12007439 divides  2^ 6003719 -1 .. csec = 16
  k = 6 . LOG = 7.5**, 36022927 divides  2^ 6003821 -1 .. csec = 34
  k = 24 . LOG = 81, 144093289 divides  2^ 6003887 -1 .. csec = 112
  k = 30 . LOG = 82, 180117031 divides  2^ 6003901 -1 .. csec = 138
  k = 8 . LOG = 76, 48031433 divides  2^ 6003929 -1 .. csec = 43
  k = 14 . LOG = 79, 84056183 divides  2^ 6004013 -1 .. csec = 68
  k = 6 . LOG = 7.5**, 36024727 divides  2^ 6004121 -1 .. csec = 34
  k = 8 . LOG = 7.6**, 48033113 divides  2^ 6004139 -1 .. csec = 43
  k = 8 . LOG = 7.6**, 48033737 divides  2^ 6004217 -1 .. csec = 44
  k = 2 . LOG = 7.0**, 12008519 divides  2^ 6004259 -1 .. csec = 17
  k = 2 . LOG = 7.0**, 12008663 divides  2^ 6004331 -1 .. csec = 17
  k = 2 . LOG = 7.0**, 12008999 divides  2^ 6004499 -1 .. csec = 17
  k = 2 . LOG = 7.0**, 12009623 divides  2^ 6004811 -1 .. csec = 16
  k = 2 . LOG = 7.0**, 12010079 divides  2^ 6005039 -1 .. csec = 17
  k = 8 . LOG = 7.6**, 48041417 divides  2^ 6005177 -1 .. csec = 37
  k = 2 . LOG = 7.0**, 12010367 divides  2^ 6005183 -1 .. csec = 17
  k = 18 . LOG = 80, 108095887 divides  2^ 6005327 -1 .. csec = 82
  k = 6 . LOG = 75, 36032047 divides  2^ 6005341 -1 .. csec = 33
  k = 16 . LOG = 79, 96085937 divides  2^ 6005371 -1 .. csec = 76
  k = 30 . LOG = 82, 180161431 divides  2^ 6005381 -1 .. csec = 126
  k = 8 . LOG = 76, 48043433 divides  2^ 6005429 -1 .. csec = 41
  k = 8 . LOG = 76, 48043817 divides  2^ 6005477 -1 .. csec = 41
  k = 2 . LOG = 70, 12011183 divides  2^ 6005591 -1 .. csec = 17
  k = 8 . LOG = 76, 48045017 divides  2^ 6005627 -1 .. csec = 43
  k = 2 . LOG = 70, 12011303 divides  2^ 6005651 -1 .. csec = 16
  k = 2 . LOG = 70, 12011807 divides  2^ 6005903 -1 .. csec = 17
  k = 18 . LOG = 80, 108110287 divides  2^ 6006127 -1 .. csec = 86
$.moddata1 :
  k = 8 . LOG = 76, 48000089 divides  2^ 6000011 -1 .. csec = 42
  k = 8 . LOG = 76, 48000377 divides  2^ 6000047 -1 .. csec = 43
  k = 6 . LOG = 75, 36000319 divides  2^ 6000053 -1 .. csec = 34
  k = 6 . LOG = 75, 36000439 divides  2^ 6000073 -1 .. csec = 34
  k = 2 . LOG = 70, 12000239 divides  2^ 6000119 -1 .. csec = 17
  k = 2 . LOG = 70, 12000383 divides  2^ 6000191 -1 .. csec = 17
  k = 24 . LOG = 81, 144005593 divides  2^ 6000233 -1 .. csec = 107
  k = 2 . LOG = 70, 12000959 divides  2^ 6000479 -1 .. csec = 18
  k = 8 . LOG = 76, 48006473 divides  2^ 6000809 -1 .. csec = 40

next prime = 6003001  ,,,
k = 6 . LOG = 75, 36018007 divides  2^ 6003001 -1 .. csec = 33
divisors of n-1 = 6003000
= 1*6003000/ = 2*3001500/ = 3*2001000/ = 4*1500750/ 
= 5*1200600/ = 6*1000500/ = 8*750375/ = 9*667000/ = 10*600300/ 
= 12*500250/ = 15*400200/ = 18*333500/ = 20*300150/ 
= 23*261000/ = 24*250125/ = 25*240120/ = 29*207000/ 
= 30*200100/ = 36*166750/ = 40*150075/ = 45*133400/ 
= 46*130500/ = 50*120060/ = 58*103500/ = 60*100050/ 
= 69*87000/ = 72*83375/ = 75*80040/ = 87*69000/ = 90*66700/ 
= 92*65250/ = 100*60030/ = 115*52200/ = 116*51750/ 
= 120*50025/ = 125*48024/ = 138*43500/ = 145*41400/ 
= 150*40020/ = 174*34500/ = 180*33350/ = 184*32625/ 
= 200*30015/ = 207*29000/ = 225*26680/ = 230*26100/ 
= 232*25875/ = 250*24012/ = 261*23000/ = 276*21750/ 
= 290*20700/ = 300*20010/ = 345*17400/ = 348*17250/ 
= 360*16675/ = 375*16008/ = 414*14500/ = 435*13800/ 
= 450*13340/ = 460*13050/ = 500*12006/ = 522*11500/ 
= 552*10875/ = 575*10440/ = 580*10350/ = 600*10005/ 
= 667*9000/ = 690*8700/ = 696*8625/ = 725*8280/ = 750*8004/ 
= 828*7250/ = 870*6900/ = 900*6670/ = 920*6525/ = 1000*6003/ 
= 1035*5800/ = 1044*5750/ = 1125*5336/ = 1150*5220/ 
= 1160*5175/ = 1305*4600/ = 1334*4500/ = 1380*4350/ 
= 1450*4140/ = 1500*4002/ = 1656*3625/ = 1725*3480/ 
= 1740*3450/ = 1800*3335/ = 2001*3000/ = 2070*2900/ 
= 2088*2875/ = 2175*2760/ = 2250*2668/ = 2300*2610/ 
26 at erl. 59

next prime = 6003007  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003043  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003047  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003059  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003077  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003079  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003083  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003089  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003113  ,,,
k = 6 . LOG = 75, 36018679 divides  2^ 6003113 -1 .. csec = 33
divisors of n-1 = 6003112
= 1*6003112/ = 2*3001556/ = 4*1500778/ = 8*750389/ 
= 433*13864/ = 866*6932/ = 1732*3466/ = 1733*3464/ =2*r*(r+1).####
26 at erl. 59

next prime = 6003143  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003197  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003199  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003211  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003223  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003241  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003247  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003251  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003281  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003293  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003313  ,,,,,,,,,,,,,,,
k = 30 . LOG = 82, 180099391 divides  2^ 6003313 -1 .. csec = 132
divisors of n-1 = 6003312
= 1*6003312/ = 2*3001656/ = 3*2001104/ = 4*1500828/ 
= 6*1000552/ = 7*857616/ = 8*750414/ = 12*500276/ = 14*428808/ 
= 16*375207/ = 17*353136/ = 21*285872/ = 24*250138/ 
= 28*214404/ = 34*176568/ = 42*142936/ = 48*125069/ 
= 51*117712/ = 56*107202/ = 68*88284/ = 84*71468/ = 102*58856/ 
= 112*53601/ = 119*50448/ = 136*44142/ = 168*35734/ 
= 204*29428/ = 238*25224/ = 272*22071/ = 336*17867/ 
= 357*16816/ = 408*14714/ = 476*12612/ = 714*8408/ 
= 816*7357/ = 952*6306/ = 1051*5712/ = 1428*4204/ = 1904*3153/ 
= 2102*2856/ 26 at erl. 59

next prime = 6003323  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003331  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003341  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003379  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003407  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003409  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003419  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003443  ,
k = 2 . LOG = 70, 12006887 divides  2^ 6003443 -1 .. csec = 17
divisors of n-1 = 6003442
= 1*6003442/ = 2*3001721/ 26 at erl. 59

next prime = 6003497  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003511  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003521  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003527  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003539  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003581  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003607  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003623  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003643  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003649  ,,,,,,,,,,,
k = 22 . LOG = 81, 132080279 divides  2^ 6003649 -1 .. csec = 99
divisors of n-1 = 6003648
= 1*6003648/ = 2*3001824/ = 3*2001216/ = 4*1500912/ 
= 6*1000608/ = 7*857664/ = 8*750456/ = 9*667072/ = 12*500304/ 
= 14*428832/ = 16*375228/ = 18*333536/ = 21*285888/ 
= 24*250152/ = 28*214416/ = 32*187614/ = 36*166768/ 
= 42*142944/ = 48*125076/ = 56*107208/ = 63*95296/ 
= 64*93807/ = 72*83384/ = 84*71472/ = 96*62538/ = 112*53604/ 
= 126*47648/ = 144*41692/ = 168*35736/ = 192*31269/ 
= 224*26802/ = 252*23824/ = 288*20846/ = 336*17868/ 
= 448*13401/ = 504*11912/ = 576*10423/ = 672*8934/ 
= 1008*5956/ = 1344*4467/ = 1489*4032/ = 2016*2978/ 
26 at erl. 59

next prime = 6003659  ,,,,
k = 8 . LOG = 76, 48029273 divides  2^ 6003659 -1 .. csec = 43
divisors of n-1 = 6003658
= 1*6003658/ = 2*3001829/ = 19*315982/ = 38*157991/ 
26 at erl. 59

next prime = 6003661  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003719  ,
k = 2 . LOG = 70, 12007439 divides  2^ 6003719 -1 .. csec = 16
divisors of n-1 = 6003718
= 1*6003718/ = 2*3001859/ = 7*857674/ = 14*428837/ 
= 97*61894/ = 194*30947/ = 679*8842/ = 1358*4421/ 26 at erl. 59

next prime = 6003727  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003757  ,,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003761  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003769  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003793  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003797  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003821  ,,,
k = 6 . LOG = 75, 36022927 divides  2^ 6003821 -1 .. csec = 34
divisors of n-1 = 6003820
= 1*6003820/ = 2*3001910/ = 4*1500955/ = 5*1200764/ 
= 10*600382/ = 20*300191/ 26 at erl. 59

next prime = 6003853  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003857  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003859  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003871  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003883  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003887  ,,,,,,,,,,,,
k = 24 . LOG = 81, 144093289 divides  2^ 6003887 -1 .. csec = 112
divisors of n-1 = 6003886
= 1*6003886/ = 2*3001943/ = 7*857698/ = 14*428849/ 
= 19*315994/ = 38*157997/ = 133*45142/ = 266*22571/ 
26 at erl. 59

next prime = 6003889  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003901  ,,,,,,,,,,,,,,,
k = 30 . LOG = 82, 180117031 divides  2^ 6003901 -1 .. csec = 138
divisors of n-1 = 6003900
= 1*6003900/ = 2*3001950/ = 3*2001300/ = 4*1500975/ 
= 5*1200780/ = 6*1000650/ = 7*857700/ = 9*667100/ = 10*600390/ 
= 12*500325/ = 14*428850/ = 15*400260/ = 18*333550/ 
= 20*300195/ = 21*285900/ = 25*240156/ = 28*214425/ 
= 30*200130/ = 35*171540/ = 36*166775/ = 42*142950/ 
= 45*133420/ = 50*120078/ = 60*100065/ = 63*95300/ 
= 70*85770/ = 75*80052/ = 84*71475/ = 90*66710/ = 100*60039/ 
= 105*57180/ = 126*47650/ = 140*42885/ = 150*40026/ 
= 175*34308/ = 180*33355/ = 210*28590/ = 225*26684/ 
= 252*23825/ = 300*20013/ = 315*19060/ = 350*17154/ 
= 420*14295/ = 450*13342/ = 525*11436/ = 630*9530/ 
= 700*8577/ = 900*6671/ = 953*6300/ = 1050*5718/ = 1260*4765/ 
= 1575*3812/ = 1906*3150/ = 2100*2859/ 26 at erl. 59

next prime = 6003913  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003929  ,,,,
k = 8 . LOG = 76, 48031433 divides  2^ 6003929 -1 .. csec = 43
divisors of n-1 = 6003928
= 1*6003928/ = 2*3001964/ = 4*1500982/ = 7*857704/ 
= 8*750491/ = 14*428852/ = 28*214426/ = 29*207032/ 
= 56*107213/ = 58*103516/ = 116*51758/ = 203*29576/ 
= 232*25879/ = 406*14788/ = 812*7394/ = 1624*3697/ 
26 at erl. 59

next prime = 6003931  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003947  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003967  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003983  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6003997  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004001  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004007  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004013  ,,,,,,,
k = 14 . LOG = 79, 84056183 divides  2^ 6004013 -1 .. csec = 68
divisors of n-1 = 6004012
= 1*6004012/ = 2*3002006/ = 4*1501003/ = 7*857716/ 
= 14*428858/ = 23*261044/ = 28*214429/ = 46*130522/ 
= 92*65261/ = 161*37292/ = 322*18646/ = 644*9323/ 26 at erl. 59

next prime = 6004021  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004067  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004069  ,,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004087  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004093  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004121  ,,,
k = 6 . LOG = 75, 36024727 divides  2^ 6004121 -1 .. csec = 34
divisors of n-1 = 6004120
= 1*6004120/ = 2*3002060/ = 4*1501030/ = 5*1200824/ 
= 8*750515/ = 10*600412/ = 20*300206/ = 40*150103/ 
= 367*16360/ = 409*14680/ = 734*8180/ = 818*7340/ = 1468*4090/ 
= 1636*3670/ = 1835*3272/ = 2045*2936/ 26 at erl. 59

next prime = 6004139  ,,,,
k = 8 . LOG = 76, 48033113 divides  2^ 6004139 -1 .. csec = 43
divisors of n-1 = 6004138
= 1*6004138/ = 2*3002069/ = 7*857734/ = 14*428867/ 
= 37*162274/ = 67*89614/ = 74*81137/ = 134*44807/ = 173*34706/ 
= 259*23182/ = 346*17353/ = 469*12802/ = 518*11591/ 
= 938*6401/ = 1211*4958/ = 2422*2479/ 26 at erl. 59

next prime = 6004153  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004157  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004217  ,,,,
k = 8 . LOG = 76, 48033737 divides  2^ 6004217 -1 .. csec = 44
divisors of n-1 = 6004216
= 1*6004216/ = 2*3002108/ = 4*1501054/ = 8*750527/ 
= 211*28456/ = 422*14228/ = 844*7114/ = 1688*3557/ 
26 at erl. 59

next prime = 6004231  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004241  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004259  ,
k = 2 . LOG = 70, 12008519 divides  2^ 6004259 -1 .. csec = 17
divisors of n-1 = 6004258
= 1*6004258/ = 2*3002129/ = 13*461866/ = 26*230933/ 
26 at erl. 59

next prime = 6004277  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004283  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004289  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004301  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004307  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004309  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004321  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004331  ,
k = 2 . LOG = 70, 12008663 divides  2^ 6004331 -1 .. csec = 17
divisors of n-1 = 6004330
= 1*6004330/ = 2*3002165/ = 5*1200866/ = 10*600433/ 
26 at erl. 59

next prime = 6004333  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004337  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004343  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004351  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004367  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004373  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004379  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004387  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004393  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004429  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004457  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004459  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004463  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004499  ,
k = 2 . LOG = 70, 12008999 divides  2^ 6004499 -1 .. csec = 17
divisors of n-1 = 6004498
= 1*6004498/ = 2*3002249/ = 223*26926/ = 446*13463/ 
26 at erl. 59

next prime = 6004507  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004517  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004543  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004549  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004561  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004567  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004571  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004577  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004601  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004631  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004637  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004639  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004651  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004699  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004727  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004729  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004751  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004759  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004763  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004777  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004781  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004783  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004787  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004799  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004811  ,
k = 2 . LOG = 70, 12009623 divides  2^ 6004811 -1 .. csec = 16
divisors of n-1 = 6004810
= 1*6004810/ = 2*3002405/ = 5*1200962/ = 7*857830/ 
= 10*600481/ = 14*428915/ = 35*171566/ = 70*85783/ 
= 109*55090/ = 218*27545/ = 545*11018/ = 763*7870/ 
= 787*7630/ = 1090*5509/ = 1526*3935/ = 1574*3815/ 
26 at erl. 59

next prime = 6004813  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004837  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004877  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004879  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004891  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004897  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004903  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004949  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004951  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004963  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004981  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004987  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6004991  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005011  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005039  ,
k = 2 . LOG = 70, 12010079 divides  2^ 6005039 -1 .. csec = 17
divisors of n-1 = 6005038
= 1*6005038/ = 2*3002519/ = 13*461926/ = 26*230963/ 
= 71*84578/ = 142*42289/ = 923*6506/ = 1846*3253/ 26 at erl. 59

next prime = 6005101  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005107  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005113  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005141  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005149  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005177  ,,,,
k = 8 . LOG = 76, 48041417 divides  2^ 6005177 -1 .. csec = 37
divisors of n-1 = 6005176
= 1*6005176/ = 2*3002588/ = 4*1501294/ = 8*750647/ 
= 173*34712/ = 346*17356/ = 692*8678/ = 1384*4339/ 
26 at erl. 59

next prime = 6005183  ,
k = 2 . LOG = 70, 12010367 divides  2^ 6005183 -1 .. csec = 17
divisors of n-1 = 6005182
= 1*6005182/ = 2*3002591/ = 17*353246/ = 34*176623/ 
= 347*17306/ = 509*11798/ = 694*8653/ = 1018*5899/ 
26 at erl. 59

next prime = 6005191  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005201  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005203  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005213  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005287  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005297  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005303  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005309  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005327  ,,,,,,,,,
k = 18 . LOG = 80, 108095887 divides  2^ 6005327 -1 .. csec = 82
divisors of n-1 = 6005326
= 1*6005326/ = 2*3002663/ 26 at erl. 59

next prime = 6005339  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005341  ,,,
k = 6 . LOG = 75, 36032047 divides  2^ 6005341 -1 .. csec = 33
divisors of n-1 = 6005340
= 1*6005340/ = 2*3002670/ = 3*2001780/ = 4*1501335/ 
= 5*1201068/ = 6*1000890/ = 9*667260/ = 10*600534/ 
= 11*545940/ = 12*500445/ = 15*400356/ = 18*333630/ 
= 20*300267/ = 22*272970/ = 27*222420/ = 30*200178/ 
= 33*181980/ = 36*166815/ = 44*136485/ = 45*133452/ 
= 54*111210/ = 55*109188/ = 60*100089/ = 66*90990/ 
= 81*74140/ = 90*66726/ = 99*60660/ = 108*55605/ = 110*54594/ 
= 132*45495/ = 135*44484/ = 162*37070/ = 165*36396/ 
= 180*33363/ = 198*30330/ = 220*27297/ = 270*22242/ 
= 297*20220/ = 324*18535/ = 330*18198/ = 337*17820/ 
= 396*15165/ = 405*14828/ = 495*12132/ = 540*11121/ 
= 594*10110/ = 660*9099/ = 674*8910/ = 810*7414/ = 891*6740/ 
= 990*6066/ = 1011*5940/ = 1188*5055/ = 1348*4455/ 
= 1485*4044/ = 1620*3707/ = 1685*3564/ = 1782*3370/ 
= 1980*3033/ = 2022*2970/ 26 at erl. 59

next prime = 6005357  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005371  ,,,,,,,,
k = 16 . LOG = 79, 96085937 divides  2^ 6005371 -1 .. csec = 76
divisors of n-1 = 6005370
= 1*6005370/ = 2*3002685/ = 3*2001790/ = 5*1201074/ 
= 6*1000895/ = 7*857910/ = 10*600537/ = 14*428955/ 
= 15*400358/ = 21*285970/ = 30*200179/ = 35*171582/ 
= 42*142985/ = 70*85791/ = 105*57194/ = 210*28597/ 
26 at erl. 59

next prime = 6005381  ,,,,,,,,,,,,,,,
k = 30 . LOG = 82, 180161431 divides  2^ 6005381 -1 .. csec = 126
divisors of n-1 = 6005380
= 1*6005380/ = 2*3002690/ = 4*1501345/ = 5*1201076/ 
= 10*600538/ = 20*300269/ = 43*139660/ = 86*69830/ 
= 172*34915/ = 215*27932/ = 430*13966/ = 860*6983/ 
26 at erl. 59

next prime = 6005383  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005401  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005429  ,,,,
k = 8 . LOG = 76, 48043433 divides  2^ 6005429 -1 .. csec = 41
divisors of n-1 = 6005428
= 1*6005428/ = 2*3002714/ = 4*1501357/ = 11*545948/ 
= 13*461956/ = 22*272974/ = 26*230978/ = 44*136487/ 
= 52*115489/ = 143*41996/ = 286*20998/ = 572*10499/ 
26 at erl. 59

next prime = 6005443  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005459  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005477  ,,,,
k = 8 . LOG = 76, 48043817 divides  2^ 6005477 -1 .. csec = 41
divisors of n-1 = 6005476
= 1*6005476/ = 2*3002738/ = 4*1501369/ 26 at erl. 59

next prime = 6005497  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005533  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005569  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005579  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005591  ,
k = 2 . LOG = 70, 12011183 divides  2^ 6005591 -1 .. csec = 17
divisors of n-1 = 6005590
= 1*6005590/ = 2*3002795/ = 5*1201118/ = 10*600559/ 
= 17*353270/ = 34*176635/ = 85*70654/ = 170*35327/ 
26 at erl. 59

next prime = 6005603  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005627  ,,,,
k = 8 . LOG = 76, 48045017 divides  2^ 6005627 -1 .. csec = 43
divisors of n-1 = 6005626
= 1*6005626/ = 2*3002813/ = 11*545966/ = 22*272983/ 
26 at erl. 59

next prime = 6005647  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005651  ,
k = 2 . LOG = 70, 12011303 divides  2^ 6005651 -1 .. csec = 16
divisors of n-1 = 6005650
= 1*6005650/ = 2*3002825/ = 5*1201130/ = 7*857950/ 
= 10*600565/ = 14*428975/ = 25*240226/ = 35*171590/ 
= 50*120113/ = 70*85795/ = 175*34318/ = 350*17159/ 
26 at erl. 59

next prime = 6005663  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005687  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005717  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005719  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005749  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005759  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005789  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005849  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005851  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005861  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005863  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005869  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005887  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005891  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005893  ,,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005897  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005899  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005903  ,
k = 2 . LOG = 70, 12011807 divides  2^ 6005903 -1 .. csec = 17
divisors of n-1 = 6005902
= 1*6005902/ = 2*3002951/ = 7*857986/ = 14*428993/ 
= 271*22162/ = 542*11081/ = 1583*3794/ = 1897*3166/ 
26 at erl. 59

next prime = 6005911  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005917  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005927  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6005953  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6006029  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6006031  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6006047  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6006053  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6006067  ,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6006073  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6006079  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6006089  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6006097  ,,,,,,,,,,,,,,,,,26 at erl. 98

next prime = 6006127  ,,,,,,,,,
k = 18 . LOG = 80, 108110287 divides  2^ 6006127 -1 .. csec = 86
divisors of n-1 = 6006126
= 1*6006126/ = 2*3003063/ = 3*2002042/ = 6*1001021/ 
= 7*858018/ = 14*429009/ = 21*286006/ = 31*193746/ 
= 42*143003/ = 49*122574/ = 62*96873/ = 93*64582/ = 98*61287/ 
= 147*40858/ = 186*32291/ = 217*27678/ = 294*20429/ 
= 434*13839/ = 651*9226/ = 659*9114/ = 1302*4613/ = 1318*4557/ 
= 1519*3954/ = 1977*3038/ 26 at erl. 59

next prime = 6006137  ,,,,,,,,,,,,,,,,,26 at erl. 98
17 at erl. 24close #0
