Growth Phase
Starting from 2^0 = 1, multiply by 2 at each step. Each step changes the CRT address across seven channels. Six channels have Carmichael lambda = lcm(4,6,20,42,10,12) = 420. The seventh (mod 17) has phi(17) = 16. The full period is lcm(420, 16) = 1680.
Collapse Phase
At k = 420: CRT = (0,1,1,1,1,1,16). The mod-8 channel is zeroed (2^3 = 0 mod 8). Five channels return to 1. But mod 17 = 16: the seventh channel is not yet home. Growth to 1,576,576 takes 420 steps. The mod-17 channel needs 1680 steps for full resolution.
2^3 = 8
k = 3
mod-8 channel zeroed: 8 mod 8 = 0. First death.
2^6 = 64
k = 6
mod-9 returns: 64 mod 9 = 1. (phi(9) = 6.)
2^8 = 256
k = 8
mod-17 returns: 256 mod 17 = 1. ord(2,17) = 8.
2^10 = 1024
k = 10
mod-11 returns: 1024 mod 11 = 1. (phi(11) = 10.)
2^12 = 4096
k = 12
mod-13 returns: 4096 mod 13 = 1. (phi(13) = 12.)
2^20
k = 20
mod-25 returns: 2^20 mod 25 = 1. (phi(25) = 20.)
2^21
k = 21
mod-49 returns: 2^21 mod 49 = 1. (ord(2,49) = 21.)
2^420
k = 420
CRT = (0,1,1,1,1,1,16). Six channels resolved. mod-17 = 16 (not home). 2^420 mod 12,612,600 = 1,576,576.
2^1680
k = 1680
CRT = (0,1,1,1,1,1,1). All 7 channels resolved. Full period of Z/214,414,200. 2^1680 mod 214,414,200 = 26,801,776.