Contact
CoCalc Logo Icon
StoreFeaturesDocsShareSupport News AboutSign UpSign In
| Download

All published worksheets from http://sagenb.org

Views: 168727
Image: ubuntu2004
v = [1,2,3,..,64]

for n in v: print n, is_prime(10^n+1)
1 True 2 True 3 False 4 False 5 False 6 False 7 False 8 False 9 False 10 False 11 False 12 False 13 False 14 False 15 False 16 False 17 False 18 False 19 False 20 False 21 False 22 False 23 False 24 False 25 False 26 False 27 False 28 False 29 False 30 False 31 False 32 False 33 False 34 False 35 False 36 False 37 False 38 False 39 False 40 False 41 False 42 False 43 False 44 False 45 False 46 False 47 False 48 False 49 False 50 False 51 False 52 False 53 False 54 False 55 False 56 False 57 False 58 False 59 False 60 False 61 False 62 False 63 False 64 False
for n in v: print n, factor(10^n+1)
1 11 2 101 3 7 * 11 * 13 4 73 * 137 5 11 * 9091 6 101 * 9901 7 11 * 909091 8 17 * 5882353 9 7 * 11 * 13 * 19 * 52579 10 101 * 3541 * 27961 11 11^2 * 23 * 4093 * 8779 12 73 * 137 * 99990001 13 11 * 859 * 1058313049 14 29 * 101 * 281 * 121499449 15 7 * 11 * 13 * 211 * 241 * 2161 * 9091 16 353 * 449 * 641 * 1409 * 69857 17 11 * 103 * 4013 * 21993833369 18 101 * 9901 * 999999000001 19 11 * 909090909090909091 20 73 * 137 * 1676321 * 5964848081 21 7^2 * 11 * 13 * 127 * 2689 * 459691 * 909091 22 89 * 101 * 1052788969 * 1056689261 23 11 * 47 * 139 * 2531 * 549797184491917 24 17 * 5882353 * 9999999900000001 25 11 * 251 * 5051 * 9091 * 78875943472201 26 101 * 521 * 1900381976777332243781 27 7 * 11 * 13 * 19 * 52579 * 70541929 * 14175966169 28 73 * 137 * 7841 * 127522001020150503761 29 11 * 59 * 154083204930662557781201849 30 61 * 101 * 3541 * 9901 * 27961 * 4188901 * 39526741 31 11 * 909090909090909090909090909091 32 19841 * 976193 * 6187457 * 834427406578561 33 7 * 11^2 * 13 * 23 * 4093 * 8779 * 599144041 * 183411838171 34 101 * 28559389 * 1491383821 * 2324557465671829 35 11 * 9091 * 909091 * 4147571 * 265212793249617641 36 73 * 137 * 3169 * 98641 * 99990001 * 3199044596370769 37 11 * 7253 * 422650073734453 * 296557347313446299 38 101 * 722817036322379041 * 1369778187490592461 39 7 * 11 * 13^2 * 157 * 859 * 6397 * 216451 * 1058313049 * 388847808493 40 17 * 5070721 * 5882353 * 19721061166646717498359681 41 11 * 2670502781396266997 * 3404193829806058997303 42 29 * 101 * 281 * 9901 * 226549 * 121499449 * 4458192223320340849 43 11 * 57009401 * 2182600451 * 7306116556571817748755241 44 73 * 137 * 617 * 16205834846012967584927082656402106953 45 7 * 11 * 13 * 19 * 211 * 241 * 2161 * 9091 * 29611 * 52579 * 3762091 * 8985695684401 46 101 * 1289 * 18371524594609 * 4181003300071669867932658901 47 11 * 6299 * 4855067598095567 * 297262705009139006771611927 48 97 * 353 * 449 * 641 * 1409 * 69857 * 206209 * 66554101249 * 75118313082913 49 11 * 197 * 909091 * 5076141624365532994918781726395939035533 50 101 * 3541 * 27961 * 60101 * 7019801 * 14103673319201 * 1680588011350901 51 7 * 11 * 13 * 103 * 4013 * 21993833369 * 291078844423 * 377526955309799110357 52 73 * 137 * 1580801 * 632527440202150745090622412245443923049201 53 11 * 9090909090909090909090909090909090909090909090909091 54 101 * 109 * 9901 * 153469 * 999999000001 * 59779577156334533866654838281 55 11^2 * 23 * 331 * 4093 * 5171 * 8779 * 9091 * 20163494891 * 318727841165674579776721 56 17 * 113 * 5882353 * 73765755896403138401 * 119968369144846370226083377 57 7 * 11 * 13 * 1458973 * 909090909090909091 * 753201806271328462547977919407 58 101 * 349 * 38861 * 618049 * 11811806375201836408679635736258669583187541 59 11 * 1889 * 1090805842068098677837 * 4411922770996074109644535362851087 60 73 * 137 * 1676321 * 99990001 * 5964848081 * 100009999999899989999000000010001 61 11 * 81131 * 11205222530116836855321528257890437575145023592596037161 62 101 * 2049349 * 483128549554512237305554588359039822397307149685578249 63 7^2 * 11 * 13 * 19 * 127 * 2689 * 52579 * 459691 * 909091 * 5274739 * 189772422673235585874485732659 64 1265011073 * 15343168188889137818369 * 515217525265213267447869906815873
v = [2,4,6,..,64]

for n in v: print n, factor(10^n+1)
2 101 4 73 * 137 6 101 * 9901 8 17 * 5882353 10 101 * 3541 * 27961 12 73 * 137 * 99990001 14 29 * 101 * 281 * 121499449 16 353 * 449 * 641 * 1409 * 69857 18 101 * 9901 * 999999000001 20 73 * 137 * 1676321 * 5964848081 22 89 * 101 * 1052788969 * 1056689261 24 17 * 5882353 * 9999999900000001 26 101 * 521 * 1900381976777332243781 28 73 * 137 * 7841 * 127522001020150503761 30 61 * 101 * 3541 * 9901 * 27961 * 4188901 * 39526741 32 19841 * 976193 * 6187457 * 834427406578561 34 101 * 28559389 * 1491383821 * 2324557465671829 36 73 * 137 * 3169 * 98641 * 99990001 * 3199044596370769 38 101 * 722817036322379041 * 1369778187490592461 40 17 * 5070721 * 5882353 * 19721061166646717498359681 42 29 * 101 * 281 * 9901 * 226549 * 121499449 * 4458192223320340849 44 73 * 137 * 617 * 16205834846012967584927082656402106953 46 101 * 1289 * 18371524594609 * 4181003300071669867932658901 48 97 * 353 * 449 * 641 * 1409 * 69857 * 206209 * 66554101249 * 75118313082913 50 101 * 3541 * 27961 * 60101 * 7019801 * 14103673319201 * 1680588011350901 52 73 * 137 * 1580801 * 632527440202150745090622412245443923049201 54 101 * 109 * 9901 * 153469 * 999999000001 * 59779577156334533866654838281 56 17 * 113 * 5882353 * 73765755896403138401 * 119968369144846370226083377 58 101 * 349 * 38861 * 618049 * 11811806375201836408679635736258669583187541 60 73 * 137 * 1676321 * 99990001 * 5964848081 * 100009999999899989999000000010001 62 101 * 2049349 * 483128549554512237305554588359039822397307149685578249 64 1265011073 * 15343168188889137818369 * 515217525265213267447869906815873
v = [4,8,12,..64]

for n in v: print n, factor(10^n+1)
4 73 * 137 8 17 * 5882353 12 73 * 137 * 99990001 16 353 * 449 * 641 * 1409 * 69857 20 73 * 137 * 1676321 * 5964848081 24 17 * 5882353 * 9999999900000001 28 73 * 137 * 7841 * 127522001020150503761 32 19841 * 976193 * 6187457 * 834427406578561 36 73 * 137 * 3169 * 98641 * 99990001 * 3199044596370769 40 17 * 5070721 * 5882353 * 19721061166646717498359681 44 73 * 137 * 617 * 16205834846012967584927082656402106953 48 97 * 353 * 449 * 641 * 1409 * 69857 * 206209 * 66554101249 * 75118313082913 52 73 * 137 * 1580801 * 632527440202150745090622412245443923049201 56 17 * 113 * 5882353 * 73765755896403138401 * 119968369144846370226083377 60 73 * 137 * 1676321 * 99990001 * 5964848081 * 100009999999899989999000000010001
73*137
10001
(10^68+1)/(10^4+1)
9999000099990000999900009999000099990000999900009999000099990001
v = [8,16,24,..,64]

for n in v: print n, factor(10^n+1)
8 17 * 5882353 16 353 * 449 * 641 * 1409 * 69857 24 17 * 5882353 * 9999999900000001 32 19841 * 976193 * 6187457 * 834427406578561 40 17 * 5070721 * 5882353 * 19721061166646717498359681 48 97 * 353 * 449 * 641 * 1409 * 69857 * 206209 * 66554101249 * 75118313082913 56 17 * 113 * 5882353 * 73765755896403138401 * 119968369144846370226083377 64 1265011073 * 15343168188889137818369 * 515217525265213267447869906815873
(10^72+1)/(10^8+1)
9999999900000000999999990000000099999999000000009999999900000001
v = [16,32,..,64]

for n in v: print n, factor(10^n+1)
16 353 * 449 * 641 * 1409 * 69857 32 19841 * 976193 * 6187457 * 834427406578561 48 97 * 353 * 449 * 641 * 1409 * 69857 * 206209 * 66554101249 * 75118313082913 64 1265011073 * 15343168188889137818369 * 515217525265213267447869906815873
(10^80+1)/(10^16+1)
9999999999999999000000000000000099999999999999990000000000000001
print('in het algemeen kan alleen 10^(2^k) + 1 priem zijn')
in het algemeen kan alleen 10^(2^k) + 1 priem zijn
print('zie: http://www1.uni-hamburg.de/RRZ/W.Keller/GFN10.html')
zie: http://www1.uni-hamburg.de/RRZ/W.Keller/GFN10.html
print('of google op "fermat number base 10"')
of google op "fermat number base 10"
v = [2^k for k in range(1,25)]; v
[2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216]
for n in v: print n, is_prime(10^n+1)
2 True 4 False 8 False 16 False 32 False 64 False 128 False 256 False 512 False 1024 False 2048 False 4096 False 8192 False