ℙ — PrimeℙN: Nth prime, one-based. J’s p: family. Integral inputs; exact integer results.
ℙ⍳8 ⍝ 2x 3x 5x 7x 11x 13x 17x 19x
ℙ⍣¯1⊢ℙ⍳4 ⍝ 1x 2x 3x 4x
KℙN selects an operation; codes retain J’s values.
| K | Result |
|---|---|
¯4 |
Previous prime, strictly below N |
¯1 |
Number of primes strictly below N |
0 |
N is not prime |
1 |
N is prime |
2 |
Two-row distinct-factor/exponent table |
3 |
Repeated prime factors |
4 |
Next prime, strictly above N |
5 |
Euler’s totient |
¯1ℙ1 2 3 4 5 6 ⍝ 0x 0x 1x 2x 2x 3x
1ℙ¯1 0 1 2 3 4 ⍝ 0x 0x 0x 1x 1x 0x
4ℙ1 2 3 4 5 ⍝ 2x 3x 5x 5x 7x
5ℙ1 2 3 4 5 6 ⍝ 1x 1x 2x 2x 4x 2x
2ℙ700 ⍝ 2 3⍴2x 5x 7x 2x 2x 1x
Scalar cells; results assemble with fill. Inverse: count-below plus one. Primality testing is deterministic through 64 bits, probabilistic above that (false-positive bound 2⁻⁶⁴).
DOMAIN: invalid selector/input; previous prime at/below 2. See Factor.