Computational verification

Checking Collatz at the frontier

A running count of whole numbers, just beyond the edge of what has been verified, that have been confirmed to reach 1.

Take any positive whole number. If it is even, halve it; if it is odd, multiply by three and add one. Repeat. The Collatz conjecture says that every starting number eventually reaches 1. Nobody has proved it, but computers have checked enormous ranges: every number below $2^{71} \approx 2.36 \times 10^{21}$ has been verified in peer-reviewed work, and a long-running distributed project reports progress somewhat beyond that.

This project starts at that reported edge and checks the next consecutive integers, in batches, on a single machine. Because every smaller number is already known to reach 1, it is enough to show that each new number eventually falls below where it started. Most numbers are dismissed instantly by short, proved shortcuts; the rest have their trajectories computed exactly. Every batch produces a certificate that is checked and replayed independently before it counts.

Verified so far

The tally

Integers checked: 1 215 984
Batches completed: 87
Unresolved: 0
Last published: 2026-10-12

Starting point B (reported frontier)

2 392 518 188 130 438 742 016

Current frontier: next integer to check

2 392 518 188 130 439 958 000

B + 1 215 984

Checked interval, batch by batch (width proportional to size)

BB + 1 215 984

How each integer was settled

Even: halving at once gives a smaller number607 992 (50.0%)
One more than a multiple of 4: falls below itself in two steps303 996 (25.0%)
Two more than a multiple of 3: reached from a smaller number101 332 (8.3%)
Four more than a multiple of 9: reached from a smaller number in three steps33 777 (2.8%)
Three more than a multiple of 16: falls below itself in four steps42 221 (3.5%)
Everything else: trajectory computed exactly126 666 (10.4%)

All 87 batches

Batch	From	To (exclusive)	Integers	Certificate
1	B + 0	B + 144	144	`99d6907248aa…`
2	B + 144	B + 1 584	1 440	`cebd2cf5d6e0…`
3	B + 1 584	B + 15 984	14 400	`ab213f7ba901…`
4	B + 15 984	B + 30 384	14 400	`8a879d23f289…`
5	B + 30 384	B + 44 784	14 400	`5e68013a6ac6…`
6	B + 44 784	B + 59 184	14 400	`e8fbc86a0489…`
7	B + 59 184	B + 73 584	14 400	`d1d7e3a0f27b…`
8	B + 73 584	B + 87 984	14 400	`e9d4ccb4837b…`
9	B + 87 984	B + 102 384	14 400	`f936d6262777…`
10	B + 102 384	B + 115 984	13 600	`5f46665571ef…`
11	B + 115 984	B + 130 384	14 400	`bf87af5c756a…`
12	B + 130 384	B + 144 784	14 400	`57cb4c724b07…`
13	B + 144 784	B + 159 184	14 400	`7ba544657231…`
14	B + 159 184	B + 173 584	14 400	`e6bd0fd0d07f…`
15	B + 173 584	B + 187 984	14 400	`8bb0a9f5d5a1…`
16	B + 187 984	B + 202 384	14 400	`6d6d2cca4725…`
17	B + 202 384	B + 215 984	13 600	`c02b25bf00b1…`
18	B + 215 984	B + 230 384	14 400	`139fd4519dbe…`
19	B + 230 384	B + 244 784	14 400	`4ba4aa2a67cb…`
20	B + 244 784	B + 259 184	14 400	`5a706073ba22…`
21	B + 259 184	B + 273 584	14 400	`afeaff6687d9…`
22	B + 273 584	B + 287 984	14 400	`a93f38805904…`
23	B + 287 984	B + 302 384	14 400	`b30f7a1fb90c…`
24	B + 302 384	B + 316 784	14 400	`e5c575279089…`
25	B + 316 784	B + 331 184	14 400	`bdfe1af928a0…`
26	B + 331 184	B + 345 584	14 400	`21a0bae47f65…`
27	B + 345 584	B + 359 984	14 400	`efc79346df4b…`
28	B + 359 984	B + 374 384	14 400	`d7a449f75d5d…`
29	B + 374 384	B + 388 784	14 400	`47f5aea8eea4…`
30	B + 388 784	B + 403 184	14 400	`4f0906b51b08…`
31	B + 403 184	B + 417 584	14 400	`aec18796d34b…`
32	B + 417 584	B + 431 984	14 400	`5a0ba4aedee5…`
33	B + 431 984	B + 446 384	14 400	`8f8d87cd3476…`
34	B + 446 384	B + 460 784	14 400	`b754f01a37a4…`
35	B + 460 784	B + 475 184	14 400	`3841cf963bf1…`
36	B + 475 184	B + 489 584	14 400	`206842d532d5…`
37	B + 489 584	B + 503 984	14 400	`d93878d1b7ef…`
38	B + 503 984	B + 518 384	14 400	`88db39349c7e…`
39	B + 518 384	B + 532 784	14 400	`6c8050aa4f98…`
40	B + 532 784	B + 547 184	14 400	`e1ee463e5410…`
41	B + 547 184	B + 561 584	14 400	`4fb0023885aa…`
42	B + 561 584	B + 575 984	14 400	`b2a04af965f1…`
43	B + 575 984	B + 590 384	14 400	`358e1ea3a13a…`
44	B + 590 384	B + 604 784	14 400	`8c35d490320e…`
45	B + 604 784	B + 619 184	14 400	`62b456fcade7…`
46	B + 619 184	B + 633 584	14 400	`2f1cb39b133b…`
47	B + 633 584	B + 647 984	14 400	`f4942116e13e…`
48	B + 647 984	B + 662 384	14 400	`abec0d1ab059…`
49	B + 662 384	B + 676 784	14 400	`24605fbeccf1…`
50	B + 676 784	B + 691 184	14 400	`41ba8001fb0c…`
51	B + 691 184	B + 705 584	14 400	`b48ff69bb33e…`
52	B + 705 584	B + 719 984	14 400	`ced279235e74…`
53	B + 719 984	B + 734 384	14 400	`b5bac6dd8173…`
54	B + 734 384	B + 748 784	14 400	`bcda14cb150b…`
55	B + 748 784	B + 763 184	14 400	`4de510c0db52…`
56	B + 763 184	B + 777 584	14 400	`b0c855244bff…`
57	B + 777 584	B + 791 984	14 400	`9e34acb30c20…`
58	B + 791 984	B + 806 384	14 400	`a5026fe2c634…`
59	B + 806 384	B + 820 784	14 400	`ddc8c250faef…`
60	B + 820 784	B + 835 184	14 400	`89ae89ca08f4…`
61	B + 835 184	B + 849 584	14 400	`5c85332efc4c…`
62	B + 849 584	B + 863 984	14 400	`6222e9ee7316…`
63	B + 863 984	B + 878 384	14 400	`e451da720ab8…`
64	B + 878 384	B + 892 784	14 400	`af5d7333b13c…`
65	B + 892 784	B + 907 184	14 400	`a0a0ebedf54d…`
66	B + 907 184	B + 921 584	14 400	`d17e1e672426…`
67	B + 921 584	B + 935 984	14 400	`7ee39b73f61a…`
68	B + 935 984	B + 950 384	14 400	`d063e2ffef2f…`
69	B + 950 384	B + 964 784	14 400	`d9393ed0be9b…`
70	B + 964 784	B + 979 184	14 400	`049f894a9149…`
71	B + 979 184	B + 993 584	14 400	`a7d317be803d…`
72	B + 993 584	B + 1 007 984	14 400	`017e91f7e24d…`
73	B + 1 007 984	B + 1 022 384	14 400	`529302be8bf0…`
74	B + 1 022 384	B + 1 036 784	14 400	`e4c8e9aa0409…`
75	B + 1 036 784	B + 1 051 184	14 400	`256030aaabc8…`
76	B + 1 051 184	B + 1 065 584	14 400	`a3ec04827d44…`
77	B + 1 065 584	B + 1 079 984	14 400	`9b7f67787dbf…`
78	B + 1 079 984	B + 1 094 384	14 400	`7f4ad4395115…`
79	B + 1 094 384	B + 1 108 784	14 400	`f81f6bbd996d…`
80	B + 1 108 784	B + 1 123 184	14 400	`1bd08a4d2680…`
81	B + 1 123 184	B + 1 137 584	14 400	`2a6af196a8de…`
82	B + 1 137 584	B + 1 151 984	14 400	`eca4d0a63f6f…`
83	B + 1 151 984	B + 1 166 384	14 400	`56cc8ce7a26b…`
84	B + 1 166 384	B + 1 180 784	14 400	`07277b266253…`
85	B + 1 180 784	B + 1 195 184	14 400	`d3885d023f27…`
86	B + 1 195 184	B + 1 209 584	14 400	`69c4ed506295…`
87	B + 1 209 584	B + 1 215 984	6 400	`6f886ebbe57b…`

What this does and does not show. Every integer in the covered interval reaches 1, conditional on the author-reported base. This is a finite, conditional computational result: not a proof of the Collatz conjecture, not a reproduction of the base, and not a claim of a world first or of global frontier extension.

The starting point B is the distributed project’s reported bound ↗, observed 2026-10-11. The peer-reviewed bound is 2⁷¹, published by Bařina (2025). Other projects may be checking the same range.

Full progress record ↗Repository ↗

The machine

Live view

Live: runningLast checked 18:29:11 UTC

Local observations; checkpoints are provisional. Verified tally changes only after separate publication.

Current batch

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This session

158 400 / 2 000 000

integers requested in the current run

Recently finished batches

Batch 9814 400 integerscommitted18:26:45 UTC
Batch 9714 400 integerscommitted18:23:18 UTC
Batch 9614 400 integerscommitted18:19:54 UTC
Batch 9514 400 integerscommitted18:16:34 UTC
Batch 9414 400 integerscommitted18:13:16 UTC
Batch 9314 400 integerscommitted18:10:02 UTC
Batch 9214 400 integerscommitted18:06:48 UTC
Batch 9114 400 integerscommitted18:03:35 UTC
Batch 9014 400 integerscommitted18:00:16 UTC
Batch 8914 400 integerscommitted17:57:00 UTC
Batch 8814 400 integerscommitted17:53:52 UTC
Batch 876 400 integerscommitted13:19:16 UTC
Batch 8614 400 integerscommitted13:16:24 UTC
Batch 8514 400 integerscommitted13:13:33 UTC
Batch 8414 400 integerscommitted13:10:46 UTC
Batch 8314 400 integerscommitted13:08:01 UTC
Batch 8214 400 integerscommitted13:05:16 UTC
Batch 8114 400 integerscommitted13:02:35 UTC
Batch 8014 400 integerscommitted12:59:55 UTC
Batch 7914 400 integerscommitted12:57:19 UTC

Live status is informational. Only batches that have been verified and published count towards the tally.