Each shrine has a holy number. They will give you buffs or boons for giving them their holy number in gray scrap. Buffs/boons are temporary.
Here is a list of the holy numbers:

• Each shrine can only be used three times.
  
• You can find recipes by talking to tutorial smith (the robot that appears at the beginning of each run).
  
• Some recipes have multiple items or results that they can give.

If a recipe gives an odd result, add it in the comment section.
I have only added positive, non-temporary results on here.
Gy = Grey Scrap
Re = Red Archaic Scrap
Gr = Green Archaic Scrap
Bl = Blue Archaic Scrap

Tyr
Most of the time Tyr only gives temporary buffs.

• 15 Gy, 1 Bl = Aura Bolts, Big Bolt, Wrecking Shell, Triple shot, Buzz saw Gun
  
• 15 Gy, 1 Re = Wrecking Shell, Aura Bolts, Lil' Tyr, Mega Attack. Shoot Orb
  
• 15 Gy, 1 Gr = Aura Bolts, Mega Attack, Laser (alt weapon), Triple Shot
  
• 57 Gy, 1 Bl = Lil' Tyr

Zurvan

• 5 Gy = Full Health
  
• 10 Gy = Artifact Map, Boss Map, Cave Map, Factory Map, Buried City Map
  
• 15 Gy, 1 Re = Lil' Zurvan, Health Vorb
  
• 10 Gy, 1 Re = Explorb
  
• 10 Gy, 1 Bl = Mega Health, Artifact Map (Map 0), attractor helm, Search Burst
  
• 10 Gy, 1 Gr = Health Vorb, Mega Health

Hephaestus

• 1 Re, 1 Gr, 1 Bl = Increases energy by 3
  
• 3 Re = Remakes you, Radial Bolts
  
• 3 Re, 3 Gr, 3 Bl = Remakes you
  
• 12 Gy, 1 Bl = Tri Orb, Lil' Phaestus, Scrap Vorb
  
• 36 Gy = Health Vorb
  
• 12 Gy, 1 Gr = Artifice Helm
  
• 12 Gy, 1 Re = Energy Vorb, Celestial Charge

Wadjet Mikail

• 7 Gy = Shield
  
• 14 Gy, 1 Bl = Speed shell, Master Map
  
• 21 Gy, 1 Bl = Lil' Wadjet
  
• 14 Gy, 1 Gr = Mega speed
  
• 14 Gy, 1 Re = Hunter Killer

Buluc Chabtan

• 16 Gy, 1 Bl = Lil' Buluc, Scatter Gun (alt weapon), Shoot Orb, Machine gun, Wave Bomb
  
• 16 Gy, 1 Re = Tri Shot Orb, Lil' Buluc
  
• 14 Gy = Remakes you
  
• 99 Gy = More Attack speed (maybe temp.)
  
• 1 Gr = Remakes you

Orphiel

• 9 Gy = Nanobots
  
• 63 Gy = 21 Nanobots
  
• 9 Gy, 1 Re = Shoot Orb, Explorb, Shield Orb
  
• 18 Gy, 1 Gr = Royal Orb
  
• 9 Gy, 1 Gr = Scrap Vorb
  
• 9 Gy, 1 Bl = Energy Vorb
  
• 18 Gy, 2 Bl = Tri Orb
  
• 18 Gy, 2 Gr = Tri Orb
  
• 18 Gy, 1 Re = Mothorb, Lil' Orphy

This is guide is basically archived at this point, I have stopped updating it.