First thing: Omega does not train at double speed, that is standard CCP Marketing misleadings. Omega train at normal speed (how it was before Eve’s fall to F2P level), and Alpha trains at half speed.
SP/min = Skill Points Per Minute from attributes (=when you use your skill queue to train skills).
Primary = the skills primary attribute.
Secondary = the skills secondary attribute.
SP/min = Primary + Secondary/2 {Alpha: 0.5 * (Primary + Secondary/2}.
Minimum attributes: 17, 17.
Unmapped attributes ignoring Charisma: 20, 20.
Maximum attributes w/o Cerebral: 32, 26.
Maximum attributes w Cerebral: 44, 38.
There is a trivial 0 SP/month floor for people who forget to start a skill or a capped Alpha. Minimum below refers to minimum attributes, with alpha in {} after Omega.
Month is always 30 days, matching payment durations in Eve.
Minimum SP/month: (17+17/2) * 60 * 24 * 30 = 1,101,600 {550,800}.
Unmapped SP/month: (20 + 20/2) * 60 * 24 * 30 = 1,296,000 {648,000}.
Maximum SP/month w/o Cerebral: (32 + 26/2) * 60 * 24 * 30 = 1,944,000 {972,000}.
Maximum SP/month w Cerebral: (44 + 38/2) * 60 * 24 * 30 = 2,721,600 {1,360,800}.
An uncapped alpha buying 1 month Omega, gets a 100% boost to their trained SP, which as seen above can vary by 810,000 SP. Dependent on remap, what skills are trained over the 30 days, implants and cerebrals used.
A soft capped Alpha (5 mill SP but still having alpha skills available to train) buying 1 month of Omega can get another 1,101,600 to 2,721,600 SP.
An Omega understanding their attributes gives them SP, can increase SP/month by 1,425,600 (more if not ignoring Charisma).