Exact reference · personal field record
Pattern Atlas
Every named pattern the rarity engine recognises, with the exact number of matches across all 1,000,001 supported numbers. The knowledge is never locked; Daily Specimens simply add a personal “recorded” layer on this device.
Every definition and exact count stays public. The checkmarks are only your personal field record, stamped when a Daily Specimen naturally carries the pattern.
Saved on this device · manual analysis and simulations never stamp the atlas
Only Daily Specimens add discoveries. Sorting by probability does not change your next roll’s odds. Waiting times are averages, not guarantees.
Back up or restore your collection
Restores the collection and up to 1,000 daily specimens. It does not transfer an account or browser identity. When backups overlap, existing daily specimens stay and sightings use the larger count.
Research families
A completed family becomes a Research Seal. Select one to filter the atlas.
Repetition
0 of 8 personally recorded · 8 shown
Repeating Digit Numbers
A repdigit is a number whose digits are all the same, such as 7, 77, 777 or 444444. They are among the rarest visual patterns because every digit is locked to one value.
22,222 rolls on average
Next 30 daily rolls: 1 in 741
Five or More of One Digit
Five of a kind: one digit appears at least five times in the number, as in 888880 or 292222. Only six-digit numbers can reach this without being a full repdigit.
2,053 rolls on average
Next 30 daily rolls: 1.45%
Quadruple Digits
A quadruple number contains exactly four copies of one digit, like 4441 or 727772. Four of a kind is the point where repetition stops looking like coincidence.
88 rolls on average
Next 30 daily rolls: 28.98%
Triple Digits
A triple contains exactly three copies of one digit, such as 8188 or 636306. It is the most common form of strong repetition — and the first one most people notice.
7 rolls on average
Next 30 daily rolls: 98.84%
Double Pair Numbers
A double pair has two different digits appearing twice each, like 3388 or 271721. It is the digit equivalent of two pair in poker.
4 rolls on average
Next 30 daily rolls: 99.95%
Numbers With One Repeated Digit
The mildest form of repetition: exactly one digit appears twice, and every other digit is distinct — as in 1231 or 405067.
2 rolls on average
Next 30 daily rolls: 100.00%
Adjacent Digit Runs
A run is three or more identical digits sitting next to each other, like the 777 inside 27773. Adjacency is what makes a run read as deliberate.
28 rolls on average
Next 30 daily rolls: 66.59%
Numbers Built From Two Digits
These numbers use only two different digits across four or more places, like 9119 or 303033. The whole number is drawn from a two-symbol alphabet.
233 rolls on average
Next 30 daily rolls: 12.11%
Symmetry
0 of 1 personally recorded · 1 shown
Sequences
0 of 8 personally recorded · 8 shown
Ascending Sequence Numbers
Every digit is exactly one higher than the one before it: 123, 4567, 456789. There are only a few dozen such numbers in the entire range.
45,455 rolls on average
Next 30 daily rolls: 1 in 1,516
Descending Sequence Numbers
Each digit is exactly one lower than the previous: 321, 6543, 987654. The mirror image of an ascending sequence, and just as scarce.
38,462 rolls on average
Next 30 daily rolls: 1 in 1,283
Ascending Digit Runs
A partial climb: somewhere in the number sit three or more digits each one higher than the last, as in the 456 inside 74560.
35 rolls on average
Next 30 daily rolls: 58.42%
Descending Digit Runs
Three or more digits each one lower than the last, appearing anywhere in the number — the 543 inside 15432, for instance.
34 rolls on average
Next 30 daily rolls: 59.67%
ABAB Pattern Numbers
Two digits taking strict turns: 5252, 8080, 393939. The pattern repeats with period two from the first digit to the last.
4,115 rolls on average
Next 30 daily rolls: 1 in 138
ABCABC Pattern Numbers
A three-digit block written twice: 146146, 707707, 989989. Every six-digit number of this form is a three-digit number multiplied by 1001.
1,122 rolls on average
Next 30 daily rolls: 2.64%
Alternating Odd and Even Digits
Odd, even, odd, even — or the reverse — all the way through, as in 385274 or 1614. The digits themselves are free; only their parity is constrained.
29 rolls on average
Next 30 daily rolls: 65.52%
Zigzag Digit Numbers
Every comparison changes direction: up, down, up, down — or the reverse. In 792619 the path is 7 < 9 > 2 < 6 > 1 < 9.
7 rolls on average
Next 30 daily rolls: 98.77%
Digit Arithmetic
0 of 2 personally recorded · 2 shown
Harshad Numbers
A Harshad — or Niven — number is divisible by the sum of its own digits. 18 works because 1 + 8 = 9 and 18 ÷ 9 = 2.
10 rolls on average
Next 30 daily rolls: 95.06%
Happy Numbers
Square each digit, add them up, repeat. If you eventually reach 1 the number is happy; if not, you fall into a cycle. 19 → 82 → 68 → 100 → 1.
7 rolls on average
Next 30 daily rolls: 99.03%
Number Theory
0 of 9 personally recorded · 9 shown
Prime Numbers
A prime has no divisors other than 1 and itself. They are the building blocks every other number is assembled from.
13 rolls on average
Next 30 daily rolls: 91.39%
Semiprime Numbers
A semiprime is a product of exactly two primes, counted with multiplicity — 15 = 3 × 5, and 49 = 7 × 7 counts too.
5 rolls on average
Next 30 daily rolls: 99.92%
Perfect Squares
A perfect square is some whole number times itself: 144 = 12², 10000 = 100². The range ends neatly on 1,000,000 = 1000².
999 rolls on average
Next 30 daily rolls: 2.96%
Perfect Cubes
A perfect cube is a whole number raised to the third power: 216 = 6³, 970299 = 99³. There are only about a hundred in the entire range.
9,901 rolls on average
Next 30 daily rolls: 1 in 331
Powers of Two
Each power of two is double the last: 1, 2, 4, 8, 16, and on up through 1024, 65536 and 524288. Doubling exhausts the range in only twenty steps.
50,000 rolls on average
Next 30 daily rolls: 1 in 1,667
Fibonacci Numbers
Each Fibonacci number is the sum of the two before it: 1, 1, 2, 3, 5, 8, 13 … reaching 832040 before the range runs out.
33,333 rolls on average
Next 30 daily rolls: 1 in 1,112
Triangular Numbers
A triangular number counts the dots in a triangle: 1, 3, 6, 10, 15, 21 — each one the running total 1 + 2 + … + k.
707 rolls on average
Next 30 daily rolls: 4.16%
Factorial Numbers
A factorial multiplies together every whole number up to k: 5! = 120, 7! = 5040, 9! = 362880. The next one after that already overshoots a million.
111,111 rolls on average
Next 30 daily rolls: 1 in 3,704
Highly Divisible Numbers
These numbers have at least a hundred distinct divisors — the opposite extreme from primes, which have exactly two.
356 rolls on average
Next 30 daily rolls: 8.09%
Encodings
0 of 3 personally recorded · 3 shown
Binary Palindromes
Written in base two, these numbers read the same forwards and backwards. 9 is 1001, and 585 is 1001001001.
501 rolls on average
Next 30 daily rolls: 5.82%
Binary Repunits
These are the numbers one short of a power of two — 3, 7, 15, 31, 63, 1023 — whose binary form is nothing but ones.
55,556 rolls on average
Next 30 daily rolls: 1 in 1,852
Hexadecimal Repdigits
In base sixteen every digit is the same: 255 is FF, 4095 is FFF, and 43690 is AAAA.
16,949 rolls on average
Next 30 daily rolls: 1 in 565