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This guide is for those who do not have access to CFW or homebrew. If you have CFW or homebrew, you can start RNGing right away! Refer to the appropriate guide for the method you want to use.
There are two ways to find egg seeds. If you have never collected or rejected an egg at the nursery, use the 8 Magikarp method. The Eevee gift egg does not count. Otherwise, use the 127 Magikarp method.
Step 1: Setup for 127 Magikarp Method
If you have never accepted or rejected an egg at the nursery, skip to the 8 Magikarp method instead.
The gift Eevee egg from the nursery does not count!
Get two Magikarp, one female and one male, of different natures. Note which gender has which nature.
For faster egg generation, use Magikarps of different languages and different OT/TIDs. The Oval Charm helps eggs generate faster.
Get 2 everstones for both Magikarp to hold.
Step 2: Finding Egg Seeds (127 Magikarp Method)
Deposit the Magikarp, both holding everstones, into the nursery.
Run around until there’s an egg ready to pick up.
Save the game before picking up the egg. This step is very important!
Accept the egg and hatch it. Check its nature and compare it to the parents' natures.
If it matches the male Magikarp, note 0.
If it matches the female Magikarp, note 1.
Soft reset with L + R + Start to when the egg was ready to pick up.
Reject the egg this time. Repeat from #2 until you have 127 0s or 1s noted down in order. Soft reset to be back to your last egg again.
Open 3DSRNGTool, click on "Tools" then "Gen7 Egg Seed Finder". Copy/paste or type in your list of 0s and 1s.
Click "Go!" and wait for the search to finish. It shouldn't take long and you will get one result.
Step 3: Verifying Egg Seeds (127 Magikarp Method)
The egg seeds given are from before you started collecting/rejecting the 127 eggs. Now find what egg seed you are currently on.
In 3DSRNGTool, input your egg seeds into the "Current Status" area in order. Fill out "Parents Information" according to the Magikarp you used.
Click on "Frame Range" and input 123 as the starting number. Then click "Calculate".
To double-check the correct frame, reject the egg and remove the Magikarp from the nursery. Save your game!
Replace both Magikarp back into the nursery, but ensure neither is holding anything.
Run around until an egg is ready and accept it.
Hatch the egg and check if the nature matches frame 123 or 124. If it does, congrats! You now know your egg seeds and can continue with egg RNG.
If the nature does not match, your egg seeds were incorrect. You will need to redo the 127 eggs to get the correct seeds.
Right-click on the frame that matched and choose "Set as Current Status" to update the "Current Status" with your egg seeds.
For this method, you must not have rejected or accepted an egg from the nursery.
The gift Eevee egg does not count!
Get a Magikarp and a Ditto of the same language.
Save your game, then deposit both Pokémon into the nursery. Ensure neither is holding an item.
Step 2: Finding Egg Seeds (8 Egg Method)
Collect 8 eggs in a row and hatch them. Do NOT save your game or reject any eggs during this process.
Open 3DSRNGTool, click on "Tools" then "Gen7 Egg Seed Finder".
Choose the 8 natures you got in order from the dropdown list. There should be 8 numbers in the "Nature List".
Click "Search", and when it's done, you will have your egg seeds.
Step 3: Verifying Egg Seeds (8 Egg Method)
The egg seeds given are from before you started collecting the 8 eggs. Now verify that the egg seed you got is correct.
In 3DSRNGTool, input your egg seeds into the "Current Status" area in order. Fill out "Parents Information" according to the Magikarp and Ditto you used.
Click on "Egg Number Range", set the initial number to 1, then click "Calculate".
Check the 8 eggs you hatched against the 8 eggs info in the output. If the natures and genders match for all 8 eggs, you have the correct egg seeds.
If they do not match, redo the 8 eggs. Double-check that the correct natures are entered in the order you accepted the eggs.