Sunday, January 09, 2005

factorint precprime

The factorization of the integer preceding the first prime less than a given power of two.

? for(i=3,1000,print(i," ",factorint(precprime(2^i)-1)," ",gettime()))

exponentpreceding primefactorizationmilliseconds
3-1[2, 1; 3, 1]0
4-3[2, 2; 3, 1]0
5-1[2, 1; 3, 1; 5, 1]0
6-3[2, 2; 3, 1; 5, 1]0
7-1[2, 1; 3, 2; 7, 1]0
8-5[2, 1; 5, 3]0
9-3[2, 2; 127, 1]0
10-3[2, 2; 3, 1; 5, 1; 17, 1]0
11-9[2, 1; 1019, 1]0
12-3[2, 2; 3, 1; 11, 1; 31, 1]0
13-1[2, 1; 3, 2; 5, 1; 7, 1; 13, 1]0
14-3[2, 2; 3, 2; 5, 1; 7, 1; 13, 1]0
15-19[2, 2; 3, 1; 2729, 1]0
16-15[2, 4; 3, 2; 5, 1; 7, 1; 13, 1]0
17-1[2, 1; 3, 1; 5, 1; 17, 1; 257, 1]0
18-5[2, 1; 53, 1; 2473, 1]0
19-1[2, 1; 3, 3; 7, 1; 19, 1; 73, 1]0
20-3[2, 2; 3, 3; 7, 1; 19, 1; 73, 1]0
21-9[2, 1; 1048571, 1]0
22-3[2, 2; 3, 1; 5, 2; 11, 1; 31, 1; 41, 1]0
23-15[2, 4; 524287, 1]0
24-3[2, 2; 3, 1; 23, 1; 89, 1; 683, 1]0
25-39[2, 3; 29, 1; 61, 1; 2371, 1]0
26-5[2, 1; 479, 1; 70051, 1]0
27-39[2, 3; 11, 1; 101, 1; 15101, 1]0
28-57[2, 1; 3, 1; 7, 1; 11, 1; 581029, 1]0
29-3[2, 2; 7, 1; 73, 1; 262657, 1]0
30-35[2, 2; 7, 1; 2341, 1; 16381, 1]0
31-1[2, 1; 3, 2; 7, 1; 11, 1; 31, 1; 151, 1; 331, 1]0
32-5[2, 1; 5, 1; 19, 1; 22605091, 1]0
33-9[2, 1; 4294967291, 1]10
34-41[2, 1; 79, 1; 108733349, 1]0
35-31[2, 5; 3, 2; 7, 1; 11, 1; 31, 1; 151, 1; 331, 1]0
36-5[2, 1; 5, 1; 6871947673, 1]0
37-25[2, 1; 3, 1; 15473, 1; 1480417, 1]0
38-45[2, 1; 3, 1; 7, 2; 233, 1; 409, 1; 9811, 1]0
39-7[2, 3; 3, 3; 5, 1; 7, 1; 13, 1; 19, 1; 37, 1; 73, 1; 109, 1]0
40-87[2, 3; 3, 2; 1487, 1; 10269667, 1]0
41-21[2, 1; 5, 1; 43, 1; 5939, 1; 861089, 1]0
42-11[2, 2; 13, 1; 84577817521, 1]10
43-57[2, 1; 5, 2; 7, 1; 23, 1; 1092682363, 1]0
44-17[2, 1; 7, 1; 4583, 1; 7993, 1; 34303, 1]0
45-55[2, 3; 3, 1; 19, 1; 77158710721, 1]0
46-21[2, 1; 3, 1; 263, 1; 44593627489, 1]0
47-115[2, 2; 3, 1; 7, 1; 1675446289943, 1]10
48-59[2, 2; 797, 1; 2459, 1; 35905663, 1]0
49-81[2, 1; 5, 1; 223, 1; 252443925301, 1]10
50-27[2, 2; 3, 1; 6637, 1; 40123, 1; 352333, 1]0
51-129[2, 1; 701, 1; 1531, 1; 1049075089, 1]0
52-47[2, 4; 11, 1; 167, 1; 239, 1; 641110271, 1]10
53-111[2, 4; 5, 1; 61, 1; 23563, 1; 78332027, 1]0
54-33[2, 1; 3, 1; 5, 2; 486391, 1; 246912443, 1]0
55-55[2, 3; 3, 3; 709, 1; 235260911423, 1]10
56-5[2, 1; 5, 1; 1871, 1; 2207, 1; 2621, 1; 665789, 1]0
57-13[2, 1; 3, 1; 24019198012642643, 1]0
58-27[2, 2; 3, 1; 24019198012642643, 1]0
59-55[2, 3; 3, 1; 24019198012642643, 1]10
60-93[2, 1; 3, 1; 31, 1; 375983, 1; 16486124939, 1]10
61-1[2, 1; 3, 2; 5, 2; 7, 1; 11, 1; 13, 1; 31, 1; 41, 1; 61, 1; 151, 1; 331, 1; 1321, 1]0
62-57[2, 1; 3, 2; 1289, 1; 198762435067123, 1]0
63-25[2, 1; 3, 4; 17, 1; 23, 1; 319279, 1; 456065899, 1]10
64-59[2, 2; 11, 1; 137, 1; 547, 1; 5594472617641, 1]0
65-49[2, 1; 3, 3; 47, 1; 3384529, 1; 4294967291, 1]10
66-5[2, 1; 47, 1; 239831, 1; 3273004044197, 1]0
67-19[2, 2; 3, 2; 1409, 1; 2909351640045667, 1]10
68-23[2, 3; 47, 1; 239831, 1; 3273004044197, 1]0
69-19[2, 2; 3, 1; 41, 1; 239, 1; 5020034445340559, 1]10
70-35[2, 2; 13, 1; 463, 1; 5113, 1; 2854273, 1; 3360037, 1]0
71-231[2, 3; 709, 1; 185123, 1; 2248708131661, 1]10
72-93[2, 1; 3, 1; 251, 1; 3135701515849698017, 1]10
73-69[2, 1; 17, 1; 31, 1; 8960847216071433043, 1]0
74-35[2, 2; 61, 1; 523, 1; 242819, 1; 283007, 1; 2154013, 1]10
75-97[2, 1; 3, 2; 5, 1; 11, 1; 23, 1; 157, 1; 4229021, 1; 2498890063, 1]10
76-15[2, 4; 3, 3; 5, 1; 7, 1; 13, 1; 17, 1; 19, 1; 37, 1; 73, 1; 109, 1; 241, 1; 433, 1; 38737, 1]0
77-33[2, 1; 613, 1; 14629, 1; 70729, 1; 135559, 1; 878777, 1]10
78-11[2, 2; 13, 1; 21407, 1; 271506673682994863, 1]10
79-67[2, 2; 3, 1; 5, 1; 29, 1; 347392476900755509973, 1]0
80-65[2, 1; 5, 1; 19, 1; 283, 1; 2192857859, 1; 10252956977, 1]40
81-51[2, 2; 5, 2; 24178516392292583494123, 1]10
82-57[2, 1; 3, 1; 7, 1; 115135792344250397591063, 1]10
83-55[2, 3; 3, 1; 1873, 1; 6247, 1; 98299, 1; 540877, 1; 647771, 1]10
84-35[2, 2; 5, 1; 7, 1; 23, 1; 139, 1; 687839617, 1; 62829235873, 1]10
85-19[2, 2; 3, 2; 926902397, 1; 1159346153407711, 1]50
86-35[2, 2; 47, 1; 193, 1; 307, 1; 4463, 1; 108637, 1; 14325884401, 1]10
87-67[2, 2; 3, 1; 5, 1; 109, 1; 23473, 1; 328687, 1; 3066766765499, 1]10
88-299[2, 2; 11, 1; 23, 1; 2617, 1; 116857175046309048289, 1]10
89-1[2, 1; 3, 1; 5, 1; 17, 1; 23, 1; 89, 1; 353, 1; 397, 1; 683, 1; 2113, 1; 2931542417, 1]0
90-33[2, 1; 3, 1; 5, 1; 11, 1; 3751333452379940226967043, 1]10
91-45[2, 1; 11, 1; 479, 1; 5237, 1; 8753, 1; 173357, 1; 29565860677, 1]10
92-83[2, 2; 17, 1; 43, 1; 7649, 1; 30161, 1; 49639, 1; 147879785303, 1]0
93-25[2, 1; 3, 2; 550195573015724566621832987, 1]10
94-3[2, 2; 3, 1; 5, 1; 47, 1; 277, 1; 1013, 1; 1657, 1; 30269, 1; 178481, 1; 2796203, 1]10
95-15[2, 4; 127, 1; 911, 1; 8191, 1; 112901153, 1; 23140471537, 1]10
96-17[2, 1; 17, 1; 41, 1; 2503, 1; 11927401, 1; 1903750979809649, 1]30
97-141[2, 1; 5, 1; 7, 1; 30427, 1; 421493, 1; 176507042656349189, 1]50
98-51[2, 2; 3, 1; 11489, 1; 2298667203825814187296369, 1]10
99-115[2, 2; 3, 2; 11, 1; 23, 1; 103, 1; 216901, 1; 3114926258434939853, 1]10
100-15[2, 4; 3, 2; 5, 1; 7, 1; 13, 1; 17, 1; 97, 1; 193, 1; 241, 1; 257, 1; 673, 1; 65537, 1; 22253377, 1]10
101-69[2, 1; 2733092861843, 1; 463815415102075087, 1]150
102-33[2, 1; 3, 1; 5, 1; 3319, 1; 15761, 1; 3231076804495048272311, 1]10
103-97[2, 1; 3, 1; 5, 1; 19, 1; 17174671, 1; 131111671, 1; 7901051977843, 1]130
104-17[2, 1; 7, 1; 17, 1; 85220208418704497579610299521, 1]10
105-13[2, 1; 3, 1; 37, 2; 47, 1; 20773, 1; 26497, 1; 25507717, 1; 7483925773, 1]10
106-117[2, 1; 3, 1; 2593891, 1; 5212866077423626108151101, 1]30
107-1[2, 1; 3, 1; 107, 1; 6361, 1; 69431, 1; 20394401, 1; 28059810762433, 1]10
108-59[2, 2; 1233003839411, 1; 65798366413329190859, 1]160
109-31[2, 5; 3, 1; 5, 1; 17, 1; 53, 1; 157, 1; 1613, 1; 2731, 1; 8191, 1; 858001, 1; 308761441, 1]10
110-21[2, 1; 3, 2; 29, 1; 149, 1; 19801, 1; 842860357178749786904309, 1]10
111-37[2, 1; 3, 1; 5, 1; 8209, 1; 10541878544960465400841548563, 1]0
112-75[2, 2; 3, 1; 5, 1; 8209, 1; 10541878544960465400841548563, 1]10
113-133[2, 1; 3, 1; 249229, 1; 6944479252059789228019875067, 1]20
114-11[2, 2; 13, 1; 12853, 1; 31075037007432132746802580237, 1]0
115-67[2, 2; 3, 1; 5, 2; 353, 1; 96233, 1; 60884249347, 1; 66945988795223, 1]70
116-3[2, 2; 3, 2; 7, 1; 571, 1; 32377, 1; 174763, 1; 524287, 1; 1212847, 1; 160465489, 1]20
117-279[2, 3; 20769187434139310514121985316880349, 1]20
118-5[2, 1; 29, 1; 4729, 1; 264331, 1; 120282553, 1; 38105831644971763, 1]70
119-69[2, 1; 29, 1; 344064569, 1; 33304394189535351753233609, 1]220
120-119[2, 3; 7, 1; 17, 1; 107, 2; 443, 1; 588365753, 1; 467890108350253093, 1]90
121-73[2, 1; 3, 2; 71, 1; 1063, 1; 183033847, 1; 10691384514931340478341, 1]160
122-3[2, 2; 3, 2; 5, 2; 7, 1; 11, 1; 13, 1; 17, 1; 31, 1; 41, 1; 61, 1; 151, 1; 241, 1; 331, 1; 1321, 1; 61681, 1; 4562284561, 1]10
123-67[2, 2; 3, 1; 5, 1; 47, 1; 109, 1; 34595041857893574673792883343883, 1]10
124-59[2, 2; 11, 1; 2633, 1; 11285865197, 1; 16266011243783873888999, 1]290
125-9[2, 1; 11, 1; 19, 1; 101, 1; 75611, 1; 25593610799, 1; 520637276195190611, 1]110
126-137[2, 1; 317, 1; 3919, 1; 199974079, 1; 171214770098900531773639, 1]150
127-1[2, 1; 3, 3; 7, 2; 19, 1; 43, 1; 73, 1; 127, 1; 337, 1; 5419, 1; 92737, 1; 649657, 1; 77158673929, 1]10
128-159[2, 5; 3, 1; 10253, 1; 29333, 1; 4454477, 1; 42113237, 1; 62826870453001, 1]190
129-25[2, 1; 3, 2; 23, 1; 53, 1; 2207, 1; 73037, 1; 192419007647917553731343987, 1]10
130-5[2, 1; 23, 1; 32985101, 1; 897064739519922787230182993783, 1]60
131-69[2, 1; 19, 1; 20219, 1; 59351, 1; 59697771913750598441845212299, 1]10
132-347[2, 2; 4086621307, 1; 333069635141447143111442312491, 1]800
133-99[2, 2; 7, 1; 17, 1; 2447, 1; 23605948748323511, 1; 396029047604911001, 1]300
134-45[2, 1; 3, 1; 7, 1; 443, 1; 4241, 1; 275993039834493705010208653191503, 1]10
135-45[2, 1; 359, 1; 354034717, 1; 171348031280966828492853945787, 1]120
136-113[2, 1; 7, 1; 35023, 1; 177663425120146040044346163342727151, 1]20
137-13[2, 1; 3, 2; 15493, 1; 12611483, 1; 49537629558702115833889161799, 1]20
138-105[2, 1; 3, 1; 7, 1; 17, 1; 19, 1; 283, 1; 131267, 1; 355111, 1; 8336660597, 1; 233555095796839, 1]80
139-187[2, 2; 3, 1; 5, 2; 571, 1; 13218581, 1; 307770647134532760329414930789, 1]60
140-27[2, 2; 3, 1; 1406497, 1; 830370383, 1; 99450617953977436093324829, 1]490
141-9[2, 1; 2039, 1; 483241756040154301, 1; 1414548079303981253089, 1]840
142-111[2, 4; 3, 1; 1406497, 1; 830370383, 1; 99450617953977436093324829, 1]490
143-69[2, 1; 23, 1; 31, 1; 131, 1; 353, 1; 8893, 1; 177755497, 1; 277728329, 1; 385152161919299, 1]410
144-83[2, 2; 1700143, 1; 3279245510308636264940025379136984581, 1]20
145-151[2, 3; 3, 1; 5, 1; 67, 1; 798006697591, 1; 6951632199463154252028137287, 1]750
146-153[2, 1; 3, 1; 5, 1; 491, 1; 6055871065452986596479489008186927768087, 1]30
147-145[2, 1; 3, 1; 34301, 1; 161233, 1; 417523, 1; 174323135449, 1; 73868956290836867, 1]150
148-167[2, 3; 11, 1; 19, 1; 132657971690831, 1; 1608680259113069994569276309, 1]1730
149-31[2, 5; 3, 3; 5, 1; 7, 1; 13, 1; 17, 1; 19, 1; 37, 1; 73, 1; 97, 1; 109, 1; 241, 1; 257, 1; 433, 1; 577, 1; 673, 1; 38737, 1; 487824887233, 1]10
150-3[2, 2; 3, 1; 5, 1; 149, 1; 223, 1; 593, 1; 1777, 1; 25781083, 1; 184481113, 1; 231769777, 1; 616318177, 1]170
151-195[2, 2; 17, 1; 41977873314881172972302528513220445187727839, 1]30
152-17[2, 1; 7, 1; 17, 1; 62983, 1; 4991839, 1; 44227633, 1; 1725062259481544383088761, 1]160
153-69[2, 1; 13, 1; 17, 1; 31, 1; 833307658856201944859603543686758217126111, 1]20
154-243[2, 2; 3, 1; 5, 1; 13, 1; 1451, 1; 8093, 1; 81727, 1; 1208758919, 1; 25237278936719029457687, 1]140
155-31[2, 5; 3, 2; 7, 1; 11, 1; 31, 1; 151, 1; 251, 1; 331, 1; 601, 1; 1801, 1; 4051, 1; 100801, 1; 10567201, 1; 1133836730401, 1]40
156-143[2, 4; 13, 1; 19, 1; 21407, 1; 271506673682994863, 1; 3976729669784964390481, 1]920
157-19[2, 2; 3, 2; 565013, 1; 283127627, 1; 31722406732365708246533232867557, 1]1230
158-15[2, 4; 3, 1; 23, 1; 43, 1; 89, 1; 127, 1; 617, 1; 683, 1; 78233, 1; 35532364099, 1; 581283643249112959, 1]70
159-91[2, 2; 3, 1; 7, 1; 453553, 1; 84301218091, 1; 227524480117462744571759085503, 1]1360
160-47[2, 4; 71, 1; 40813, 1; 82963182251, 1; 379959277835395773058806460021, 1]1450
161-159[2, 5; 181, 1; 1609, 1; 15991, 1; 209060319214451, 1; 93820441463831721806779, 1]570
162-101[2, 1; 307, 1; 12209275712633, 1; 779831951475688142994810611932471, 1]6760
163-55[2, 3; 3, 3; 46020829, 1; 230938061, 1; 5093139709090657290362849823763, 1]200
164-63[2, 6; 3, 1; 2687, 1; 202029703, 1; 1113491139767, 1; 201487636602438195784363, 1]510
165-25[2, 1; 3, 2; 181, 1; 43913, 1; 458336239, 1; 713215708842851814477991561387801, 1]70
166-5[2, 1; 59573573, 1; 3218926687654133, 1; 243884697112256951372125781, 1]1580
167-135[2, 3; 2863345019, 1; 8166681291331467970489433122505775233821, 1]590
168-257[2, 1; 1385887, 1; 354062624131, 1; 381242554710766547265379727561867, 1]4270
169-643[2, 2; 3, 1; 11, 1; 2287, 1; 2478729705162984106876438083339086887890174577, 1]90
170-143[2, 4; 5, 1; 7, 1; 11, 1; 197, 1; 263, 1; 31177, 1; 69439, 1; 4323551, 1; 54561836281, 1; 9181829646439421, 1]100
171-19[2, 2; 3, 1; 373, 1; 100271, 1; 6669047866104325500594787895587024454736043, 1]20
172-95[2, 5; 5, 2; 239, 1; 1061, 1; 15263, 1; 1933374909205041859345518705365754560881, 1]30
173-55[2, 3; 3, 1; 53, 1; 811, 1; 296269, 1; 2409986827785043447, 1; 16254754097798812024831, 1]930
174-3[2, 2; 3, 1; 5, 1; 173, 1; 431, 1; 9719, 1; 101653, 1; 500177, 1; 2099863, 1; 1759217765581, 1; 2932031007403, 1]90
175-229[2, 1; 3, 1; 11, 1; 17, 1; 433, 1; 5303, 1; 1441548550921, 1; 12894888372628703287173138978851, 1]2980
176-233[2, 1; 19, 1; 100390812696683, 1; 25107395873362030653452226162419112763, 1]17300
177-339[2, 2; 43, 1; 443, 1; 269897, 1; 43417999, 1; 214540455246546428451705911111471989, 1]170
178-41[2, 1; 38461, 1; 4980680237337461514125825599796902003388949592391, 1]40
179-49[2, 1; 3, 2; 11, 1; 197, 1; 641, 1; 9619, 1; 30809, 1; 189875706144165757, 1; 544631616422353800199, 1]880
180-47[2, 4; 107, 1; 5920151, 1; 47545643, 1; 12399411469, 1; 256478448539413317884593007, 1]730
181-165[2, 1; 41, 1; 173, 1; 33861401473, 1; 6380641301623404260293530023063493488537, 1]1740
182-161[2, 1; 431, 1; 7639, 1; 669102391, 1; 40934005122337, 1; 33989017713868288731201457, 1]730
183-147[2, 2; 5, 1; 7, 1; 523, 1; 887, 1; 1035237779553371216351, 1; 182345793684253747191714659, 1]6940
184-33[2, 1; 3, 2; 347, 1; 32143427003, 1; 122130755781316693861449472063856783957039, 1]2950
185-303[2, 4; 7100671, 1; 431648090966582977399839262275441062856943835923, 1]80
186-371[2, 2; 7, 1; 11, 1; 373, 1; 881, 1; 14321, 1; 67665982492050085897207378640217002088350963, 1]70
187-85[2, 1; 3, 1; 7, 2; 84017, 1; 108161, 1; 14839871, 1; 16207518253569833, 1; 305265236392825045873, 1]510
188-125[2, 1; 5, 1; 13, 1; 397, 1; 1918919364716236391465881, 1; 3961399114926731715517839373, 1]23570
189-25[2, 1; 3, 3; 1227563, 1; 524793072442523, 1; 22555036659659199150862565259671041, 1]13800
190-11[2, 2; 11, 1; 4668159781, 1; 243343180651407107, 1; 31396526753320467221701278169, 1]6770
191-19[2, 2; 3, 1; 13, 1; 13757, 1; 3944813, 1; 379007533686944959, 1; 978152507894592399617628427, 1]4150
192-237[2, 1; 3, 1; 15739, 1; 309479, 1; 1142678623, 1; 187964352975314705242455686948494766561, 1]110
193-31[2, 5; 3, 1; 5, 1; 283, 1; 2351, 1; 3761, 1; 4513, 1; 13264529, 1; 7484047069, 1; 165768537521, 1; 140737471578113, 1]770
194-33[2, 1; 3, 1; 5, 2; 109, 1; 1120993, 1; 1369930393629556067951295927819449355800614521121, 1]40
195-135[2, 3; 7649737, 1; 2452958806703, 1; 334520246557246643906364340768470860089, 1]20650
196-15[2, 4; 3, 2; 5, 1; 7, 1; 13, 1; 17, 1; 97, 1; 193, 1; 241, 1; 257, 1; 641, 1; 673, 1; 65537, 1; 6700417, 1; 22253377, 1; 18446744069414584321, 1]120
197-75[2, 2; 137, 1; 577, 1; 6037, 1; 117496859, 1; 895581969324648364417023941445052237459747, 1]220
198-17[2, 1; 5647, 1; 6268111, 1; 5674853826681942056754247728019406574089602588439, 1]80
199-49[2, 1; 3, 1; 11, 1; 13, 1; 53, 1; 1439, 1; 23561, 1; 413407351547, 1; 6700904941889, 1; 188122098214963717375891, 1]10650
200-75[2, 2; 3, 2; 5, 2; 1973, 1; 4229, 1; 43481, 1; 4921441524559637294985132128164617176671474541, 1]40
201-55[2, 3; 3, 1; 167, 1; 373, 1; 524970661658113207, 1; 4095034364012227742853788935311573767, 1]34580
202-183[2, 3; 3, 1; 5, 1; 7, 1; 157, 1; 575359, 1; 132419253469, 1; 639720310844023611351180529144690508359, 1]16320
203-159[2, 5; 159713901631, 1; 2515338408004754911311634508555703462104415468869, 1]3150
204-167[2, 3; 701, 1; 2003, 1; 64203236540867, 1; 35651125041115722402818055390497311586431, 1]49480
205-81[2, 1; 5, 2; 23, 1; 43, 1; 83, 1; 253733, 1; 5427671, 1; 9097336384850252124159720263087428101924419, 1]60
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