Phi3(x) = x^2+x+1	
Phi3(2^3^m) = 4^3^m +2^3^m +1

factors: k*(2*3^(m+1))+1  see 3-Proths

0 7
1 73
2 262657
3 2593 * 71119 * 97685839
4 487 * 16753783618801 * 192971705688577 * 3712990163251158343
5 80191 * 97687 * 379081 * P(42) 664728004346558283448724389870269691211809 * P(90) 101213745778143742250901040788003424950068418098259161142719688891708905138274462262307761
6 39367 * 7606246033 (#2) * 263196614521 (#4) * 529063556041 (#5) * C(402) #471
7 209953 (#1) * 1299079 (#1) * C(1306) #27
8
9



(0)
7-1 = 2 * 3

(1)
73-1 = 2^3 * 3^2

(2)
262657-1 = 2^9 * 3^3 * 19

(3)
2593-1 = 2^5 * 3^4
71119-1 = 2 * 3^4 * 439
97685839-1 = 2 * 3^4 * 602999

(4)
487-1 = 2 * 3^5
16753783618801-1 = 2^4 * 3^5 * 5^2 * 19 * 9071791
192971705688577-1 =  2^9 * 3^5 * 2207 * 702773
3712990163251158343-1 = 2 * 3^6 * 7 * 382021 * 952315817

(5)
80191-1 = 2 * 3^6 * 5 * 11
97687-1 = 2 * 3^6 * 67
379081-1 = 2^3 * 3^6 * 5 * 13
P(42)-1 = 
P(90)-1 = 

(6)
39367-1 = 2 * 3^9
7606246033-1 =  2^4 * 3^8 * 7 * 11 * 941
263196614521-1 = 2^3 * 3^8 * 5 * 7^2 * 97 * 211
529063556041-1 = 2^3 * 3^8 * 5 * 2015941

(7)
209953-1 =  2^5 * 3^8
1299079-1 = 2 * 3^10 * 11



2*3^1+1 Phi3(2^3^0)
2*3^5+1 Phi3(2^3^4)
2*3^9+1 Phi3(2^3^6)

8*3^2+1 Phi3(2^3^1)

22*3^10+1 Phi3(2^3^7)

32*3^4+1 Phi3(2^3^3)
32*3^8+1 Phi3(2^3^7)



3-Proth numbers
k*3^n+1 where k is even but not divisible by 3


2
4
8

10
14
16
20
22
26
28
32
34
38
40
44
46
50
52
56
58
62
64
68
70
74
76
80
82
86
88
92
94
98

100