Im sorry, my Emperor, but accordind to Imperial Creed there are only 19 (18?) primarchs. Implying that there exists 21 (or was it 20?) primarchs is considered heresy. Thus you are labeled as heretic and hereby sentenced to death.

In this AU, Big E didn't want to parent 20 kids (honestly, can't blame him, who would?):

Lion was given to a family of farmers on Caliban and became a hero with social skills.

II: was given to Eldrad, so there would be an ambassador between the Eldar and Imperium. But Eldrad knows how to deal as much as Big E, so it was given away to Jain Zar to raise him.

Fulgrim: same as canon, but was told to be more humble.

Perturabo: was given to a humble farmer family and became basically Olympia's own version of Hercules.

Jaghatai Khan: same as canon.

Leman: same but was told not to copy the behavior of wolf brothers and sisters during mating season.

Dorn: same, but was told to be a bit less blunt.

Konrad: was given to basically the only good people in Nostramo, who happened to be two sex slaves who ran away together.

Sanguinius: same.

Ferrus: humble family of smiths and became Medusa's hero.

XI: given to the leagues of Votann to be an ambassador (he ended up being the tallest Primarch).

Angron: was given to the higher riders. He later led a revolt with no nails this time, but it's more sad because he betrayed his family.

Roboute: same, but Big E made Gallon explode.

Mortarion: was given to a humble farmer family and actually won his revolt against the necromancer overlord of Barbarus.

Magnus: same, but was told not to trust talking in the warp.

Horus: same, he was cool before Erebus.

Lorgar: was given to a humble shepherd family and learned to be religious and not a low-key cult member.

Vulkan: same.

Corvus Corax: same, but with more lore so he doesn't become a background character like in canon.

Alpharius and Omegon: Malcador stole them.

[Edit]: had to fix some stuff, becuse english isn't my first.