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Difference between revisions of "Home prime"
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The '''home prime''' of ''n'', denoted by HP(''n'') is found by concatenating the [[prime]] [[factor]]s of ''n'', repeatedly, until a prime is reached. The notion of a home prime depends on the [[base]] (except in the case where ''n'' itself is prime). | The '''home prime''' of ''n'', denoted by HP(''n'') is found by concatenating the [[prime]] [[factor]]s of ''n'', repeatedly, until a prime is reached. The notion of a home prime depends on the [[base]] (except in the case where ''n'' itself is prime). | ||
| + | Notations for other bases of 10 are HP<sub>base</sub>(n) for base ''b''. | ||
| + | |||
| + | While it is expected that every ''n'' in every base has a home prime, experimental evidence indicates that these chains can get quite long. | ||
| + | |||
| + | ==Base 10== | ||
For example, the '''home prime''' of 25 is 773 because | For example, the '''home prime''' of 25 is 773 because | ||
| − | :25 = 5×5 | + | :25 = 5 × 5 |
| − | :55 = 5×11 | + | :55 = 5 × 11 |
| − | :511 = 7×73 | + | :511 = 7 × 73 |
and finally 773 is prime. | and finally 773 is prime. | ||
The length of such chains is also of interest, in this case #HP(25) = 3. | The length of such chains is also of interest, in this case #HP(25) = 3. | ||
| − | + | ==Base 2== | |
| + | HP<sub>2</sub>(10): | ||
| + | :10<sub>10</sub> = 2 × 5 (10 × 101) | ||
| + | :21<sub>10</sub> = 3 × 7 (11 × 111) | ||
| + | :31 prime | ||
==See also== | ==See also== | ||
| Line 15: | Line 24: | ||
==External links== | ==External links== | ||
| − | *[[Wikipedia:Home prime| | + | *[[Wikipedia:Home prime|Home prime]] |
| − | [[Category: | + | [[Category:Numbers]] |
Revision as of 09:47, 8 February 2019
The home prime of n, denoted by HP(n) is found by concatenating the prime factors of n, repeatedly, until a prime is reached. The notion of a home prime depends on the base (except in the case where n itself is prime).
Notations for other bases of 10 are HPbase(n) for base b.
While it is expected that every n in every base has a home prime, experimental evidence indicates that these chains can get quite long.
Contents
Base 10
For example, the home prime of 25 is 773 because
- 25 = 5 × 5
- 55 = 5 × 11
- 511 = 7 × 73
and finally 773 is prime.
The length of such chains is also of interest, in this case #HP(25) = 3.
Base 2
HP2(10):
- 1010 = 2 × 5 (10 × 101)
- 2110 = 3 × 7 (11 × 111)
- 31 prime
