Phi7(2^7^m)
 = 64^7^m+32^7^m+16^7^m+8^7^m+4^7^m+2^7^m+1
Shanks(7)

0 127
1 4432676798593
2 6073159 * 1428389887 * 62228099977 * 58961804474844164724814095915114338093146118248375213688557057
3 14407 * 1493423 * 4725169 * C(603) #1315
4 C(4337) #423
5 8470729 (#1) * 900744038503 (#1) * 226948319644313 (#30) * C(30324) #133




[never 3^2 except prime]
[never 5] 
[others?]

(0) 2 * 7^1
127-1 = 2 * 3^2 * 7

(1) 2 * 7^2
4432676798593-1 = 2^7 * 3^2 * 7^2 * 43 * 337 * 5419

(2) 2 * 7^3
6073159-1 = 2 * 3 * 7^3 * 13 * 227
1428389887-1 = 2 * 3 * 7^3 * 11 * 63097
62228099977-1 = 2^3 * 3 * 7^4 * 41 * 26339  [ extra 7]
58961804474844164724814095915114338093146118248375213688557057-1 = 2^9 * 3 * 7^3 * 191 * 585938538228697659132042653540557810857773837273303717

(3) 2 * 7^4
14407-1 = 2 * 3 * 7^4
1493423-1 = 2 * 7^4 * 311  [ no 3]
4725169-1 = 2^4 * 3 * 7^4 * 41

(5) 2 * 7^6
8470729-1 = 2^3 * 3^2 * 7^6
900744038503-1 = 2 * 3 * 7^6 * 11 * 311 * 373
226948319644313-1 = 2^3 * 7^6 * 173 * 1393807