primeFactorization
P27191
predicate
Indicates that one entity is the decomposition of another entity into a multiset or sequence of prime factors whose product equals the original.
All labels observed (3)
| Label | Occurrences |
|---|---|
| orderFactorization | 29 |
| factorizationExample | 3 |
| primeFactorization canonical | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: primeFactorization
Generated description
Indicates that one entity is the decomposition of another entity into a multiset or sequence of prime factors whose product equals the original.
Sample triples (33)
| Subject | Object |
|---|---|
| Gaussian integers | every nonzero nonunit factors uniquely up to units and order ⓘ |
| Co1 | 2^21 via predicate surface "orderFactorization" ⓘ |
| Co1 | 3^9 via predicate surface "orderFactorization" ⓘ |
| Co1 | 5^4 via predicate surface "orderFactorization" ⓘ |
| Co1 | 7^2 via predicate surface "orderFactorization" ⓘ |
| Co1 | 11 via predicate surface "orderFactorization" ⓘ |
| Co1 | 13 via predicate surface "orderFactorization" ⓘ |
| Co1 | 23 via predicate surface "orderFactorization" ⓘ |
| Co1 | 29 via predicate surface "orderFactorization" ⓘ |
| Monster group | 2^46 · 3^20 · 5^9 · 7^6 · 11^2 · 13^3 · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71 via predicate surface "orderFactorization" ⓘ |
| Carmichael number | 561 = 3 × 11 × 17 via predicate surface "factorizationExample" ⓘ |
| Carmichael number | 1105 = 5 × 13 × 17 via predicate surface "factorizationExample" ⓘ |
| Carmichael number | 1729 = 7 × 13 × 19 via predicate surface "factorizationExample" ⓘ |
| Harada–Norton group | 2^14 via predicate surface "orderFactorization" ⓘ |
| Harada–Norton group | 3^6 via predicate surface "orderFactorization" ⓘ |
| Harada–Norton group | 5^6 via predicate surface "orderFactorization" ⓘ |
| Harada–Norton group | 7 via predicate surface "orderFactorization" ⓘ |
| Harada–Norton group | 11 via predicate surface "orderFactorization" ⓘ |
| Harada–Norton group | 19 via predicate surface "orderFactorization" ⓘ |
| Harada–Norton group | 31 via predicate surface "orderFactorization" ⓘ |
| Fischer–Griess Monster | 2^46 · 3^20 · 5^9 · 7^6 · 11^2 · 13^3 · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71 via predicate surface "orderFactorization" ⓘ |
| M | 2^46 · 3^20 · 5^9 · 7^6 · 11^2 · 13^3 · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71 via predicate surface "orderFactorization" ⓘ |
| Held group | 2^10 · 3^3 · 5^2 · 7^3 · 17 via predicate surface "orderFactorization" ⓘ |
| McLaughlin group | 2^7 · 3^6 · 5^3 · 7 · 11 via predicate surface "orderFactorization" ⓘ |
| Thompson group Th | 2^15 · 3^10 · 5^3 · 7^2 · 13 · 19 · 31 via predicate surface "orderFactorization" ⓘ |
| Janko group J4 | 2^21 × 3^3 × 5 × 7 × 11^3 × 23 × 29 × 31 × 37 × 43 via predicate surface "orderFactorization" ⓘ |
| McL | 2^7 via predicate surface "orderFactorization" ⓘ |
| McL | 3^6 via predicate surface "orderFactorization" ⓘ |
| McL | 5^3 via predicate surface "orderFactorization" ⓘ |
| McL | 7 via predicate surface "orderFactorization" ⓘ |
| McL | 11 via predicate surface "orderFactorization" ⓘ |
| McL | 23 via predicate surface "orderFactorization" ⓘ |
| SL(2,7) | 2^4·3·7 via predicate surface "orderFactorization" ⓘ |