Primarial Functions

Primarial functions are based on two types of functions : R (pronounced "er") and Я (pronounced "ya"), created by LicorneuhhOther functions/notations | Licorneuhh's numbers site (retrieved at UTC 23:00 15/12/2020)
Other functions/notations | Licorneuhh's numbers site (retrieved at UTC 11:38 16/12/2020) .
==Definition==
"Let Pi be the i-th prime number in order of natural numbers. 
R(n) = Я(n) = Pn# for all n ∈ N*, Pn# being the primorial 
R*(n) = Pn↑Pn-1↑Pn-2↑.↑.↑.↑3↑2 = PnPn-1..32 for all \(n \in \mathbb{N}\)* 
Я*(n) = 2↑3↑.↑.↑.↑Pn-2↑Pn-1↑Pn = 23..Pn-1Pn for all \(n \in \mathbb{N}\)* 
Now assume k be the amount of stars for each R*k(n) and Я*k(n). 
R*k(n) = Pn↑kPn-1↑kPn-2↑k.↑k.↑k.↑k3↑k2 for all \(n \in \mathbb{N}\)* 
Я*k(n) = 2↑k3↑k.↑k.↑k.↑kPn-2↑kPn-1↑kPn for all \(n \in \mathbb{N}\)*, 
using the Knuth's up-arrow notation."
An update has been done, replacing all the "for all \(n \in \mathbb{N}\)*" by "for all \(n \in \mathbb{N}\)\{0}", surely for more clarity and exactitude.
==Numbers==
Numbers has been coined with that functions Numbers | Licorneuhh's numbers site (retrieved at UTC 21:58 08/09/2023) :
Heads-Unprimol = Tails-Unprimol = R(1) = Я(1) = 2 
Heads-Biprimol = Tails-Biprimol = R(2) = Я(2) = 6 
Heads-Triprimol = Tails-Triprimol = R(3) = Я(3) = 30 
Heads-Tetprimol = Tails-Tetprimol = R(4) = Я(4) = 210 
Heads-Pentprimol = Tails-Pentprimol = R(5) = Я(5) = 2310 
Heads-Hexprimol = Tails-Hexprimol = R(6) = Я(6) = 30030
2-Heads-Unprimol = 2-Tails-Unprimol = R(R(1)) = Я(Я(1)) = 6
2-Heads-Biprimol = 2-Tails-Biprimol = R(R(2)) = Я(Я(2)) = 30030
2-Heads-Triprimol = 2-Tails-Triprimol = R(R(3)) = Я(Я(3)) = R(30) = Я(30) = 113# = 31 610 054 640 417 607 788 145 206 291 543 662 493 274 686 990
2-Heads-Tetprimol = 2-Tails-Tetprimol = R(R(4)) = Я(Я(4)) = R(210) = Я(210) = 1291# = 5 076 622 121 837 304 628 008 850 065 869 725 428 341 346 477 750 786 166 101 959 665 203 225 513 098 191 554 753 496 568 094 069 324 929 985 583 380 782 509 112 675 418 631 674 820 126 487 158 852 596 955 971 708 306 334 909 613 630 820 353 148 601 451 415 518 051 198 883 967 663 952 005 731 890 740 738 004 929 416 373 607 134 969 861 486 379 826 786 364 525 251 595 648 649 367 184 250 533 494 374 279 536 728 458 372 108 320 360 856 907 062 446 091 815 018 519 451 541 487 756 535 435 427 452 507 965 567 918 142 042 612 369 867 759 194 682 750 263 280 606 704 301 525 137 942 148 877 807 934 458 955 393 965 009 591 047 712 553 756 678 490 718 352 625 281 404 896 425 300 356 248 833 057 126 519 786 663 813 517 750 730 ≈ 5.0766*10543
2-Heads-Pentprimol = 2-Tails-Pentprimol = R(R(5)) = Я(Я(5)) = R(2310) = Я(2310) = 20443# ≈ 1.0495*108808
2-Heads-Hexprimol = 2-Tails-Hexprimol = R(R(6)) = Я(Я(6)) = R(30030) = Я(30030) = 350741# ≈ ??
Heads-Un-1-primol = Tails-Un-1-primol = R*(1) = Я*(1) = 2 
Heads-Bi-1-primol = R*(2) = 9 
Heads-Tri-1-primol = R*(3) = 1 953 125 
Heads-Tet-1-primol = R*(4) = 71953125 ≈ 1.286x101650582 
Heads-Pent-1-primol = R*(5) = 1171953125 ≈ 1010106.2176 
Heads-Hex-1-primol = R*(6) = 13R*(5) ≈ 101010106.2176 
Heads-Bi-2-primol = R**(2) = 3↑↑2 = 27 
Heads-Tri-2-primol = R**(3) = 5↑↑3↑↑2 = 5↑↑27 
Heads-Tet-2-primol = R**(4) = 7↑↑5↑↑3↑↑2 = 7↑↑5↑↑27 = 7↑↑R**(3) 
Heads-Pent-2-primol = R**(5) = 11↑↑7↑↑5↑↑27 = 11↑↑R**(4) 
Heads-Hex-2-primol = R**(6) = 13↑↑11↑↑7↑↑5↑↑27 = 13↑↑R**(5)
Heads-Bi-3-primol = R***(2) = 3↑↑↑2 = 7 625 597 484 987 
Heads-Tri-3-primol = R***(3) = 5↑↑↑7 625 597 484 987 
Heads-Tet-3-primol = R***(4) = 7↑↑↑5↑↑↑7 625 597 484 987 = 7↑↑↑R***(3) 
Heads-Pent-3-primol = R***(5) = 11↑↑↑7↑↑↑5↑↑↑7 625 597 484 987 = 11↑↑↑R***(4) 
Heads-Hex-3-primol = R***(6) = 13↑↑↑11↑↑↑7↑↑↑5↑↑↑7 625 597 484 987 = 13↑↑↑R***(5)
Tails-Bi-1-primol = Я*(2) = 8 
Tails-Tri-1-primol = Я*(3) = 2243 = 14134776518227074636666380005943348126619871175004951664972849610340958208 ≈ 1.413x1073 
Tails-Tet-1-primol = Я*(4) = 2378125 ≈ 101037274.5766 
Tails-Pent-1-primol = Я*(5) = 2351977326743 ≈ 101010109.14 
Tails-Hex-1-primol = Я*(6) = 235734522712143931 ≈ 101010101013.465
Tails-Bi-2-primol = Я**(2) = 2↑↑3 = 16 
Tails-Tri-2-primol = Я**(3) = 2↑↑3↑↑5 = 2↑↑(3↑3↑7625597484987) 
Tails-Tet-2-primol = Я**(4) = 2↑↑3↑↑5↑↑7 
Tails-Pent-2-primol = Я**(5) = 2↑↑3↑↑5↑↑7↑↑11 
Tails-Hex-2-primol = Я**(6) = 2↑↑3↑↑5↑↑7↑↑11↑↑13
Tails-Bi-3-primol = Я***(2) = 2↑↑↑3 = 65536 
Tails-Tri-3-primol = Я***(3) = 2↑↑↑3↑↑↑5 
Tails-Tet-3-primol = Я***(4) = 2↑↑↑3↑↑↑5↑↑↑7 
Tails-Pent-3-primol = Я***(5) = 2↑↑↑3↑↑↑5↑↑↑7↑↑↑11 
Tails-Hex-3-primol = Я***(6) = 2↑↑↑3↑↑↑5↑↑↑7↑↑↑11↑↑↑13
In general:
Heads- means R function, Tails- means Я function,
A numerical infix represents the argument of the function,
A number represents the number of stars,
And -primol goes at the end.
==References==
Category:Functions
Category:Numbers
Category:Numbers by Licorneuhh