The Elder Scrolls V Skyrim – Fastest Way to Level Up Alchemy Skill

This is completely false.

The amount of experience required to gain a point of skill level is:

k(x^1.95 )+C

• k & C = are constants depending on the skill
• x is the current skill level

The values for sneak are:

k = 2/45 c = 32/3

Here are the experience required for the first 10 levels of sneak:

1 10.71111111
2 10.83838868
3 11.045287
4 11.33015679
5 11.69186759
6 12.12955919
7 12.642538
8 13.23022354
9 13.89211712
10 14.62778195

You'll notice that there is not much difference in the experience required early on as this is not a linear curve. To go from level 49-50 will require nearly 100 experience. This may lead to the false impression that staying at lower levels means your skills go up faster, but whats really happening is if your skill level is low, its easier to improve it.

As for whether or not you can gain every perk, the amount of experience required per level is:

Current level * 25 + 75

You gain the amount of experience points equal to the level of the skill you just obtained. The game will 'bank' any extra experience towards the next level, but the maximum experience you can gain in the game is absolute. There is no way to gain all the perks as you'll top out at level 81 even if you choose to not level up at all until you max all your skills.

Here is the entire XP curve for Sneak in case you are interested:

The speed at which skill levels help you gain character levels is proportional to your current skill level - there's a certain amount of "character experience" you gain per skill experience level gained.

Therefore, getting your Alchemy from 20 to 21 will do less for your overall level than getting, say, your Archery skill from 60 to 61.

The UESP article on leveling has the formulae for this:

XP required to level up your character = (Current level + 3) * 25

Leveling a skill gives you an amount of XP equivalent to the new level of the skill.

All skills level increases gain you character level experience in the same way though, so there's not a "better" or "worse" skill for gaining ranks in in order to level your character. (This of course ignores the fact that certain skills are easier than others to gain a skill level in.)

Since you're dealing with Alchemy, the amount of skill experience you gain is tied to the value of the items you create. If you want the fastest skill experience gains, craft the most expensive potions you can, regardless of their effects. For this, I'd recommend acquiring Giant Toes and mix them with Blue Mountain Flowers and Blue Butterfly Wings.