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()))

exponent	preceding prime	factorization	milliseconds
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
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