Eurekan Weapons are the level 70 Relic Weapons for Stormblood. First released in patch 4.25, players do not need to complete any Zodiac Weapons or Anima Weapons to unlock Eurekan Weapons. Unlike with the Anima Weapon questline players who have obtained the Zodiac Zeta Weapons or the Lux Anima Weapons will not have an advantage with any step of Eurekan Weapons. However, to start the Eurekan Weapon quest chain, players must have cleared their job's Level 70 job quest, since the Eurekan Weapons are upgraded from the weapon rewarded by the job quest. As their name implies, all the upgrading activity for these relic weapons is done inside The Forbidden Land, Eureka.
Relic weapons from past expansions are not intended for combat use, but for cosmetic, achievements, and collection purposes. Weapons of similar power, for the same player level, that are much more easily obtainable and are intended for character progression can be bought with Allagan Tomestones of Poetics.
The final-stage Physeos Weapons are an exception to this rule: they provide a significant Elemental Bonus within Eureka zones, making them the best-in-slot weapons for Eureka battle content.
Lore
Deep in the Glass Ocean, the great expanse of the Far East, lies an island recorded on no navigational charts. An island that seemingly appeared one day─an island that should not be. Recognizing its potential as a trading post, the brave and ambitious ventured forth to explore and claim it, only to discover an untamed land teeming with strange, monstrous beasts...
Antiquated weapons are acquired by completing the Stormblood job quest line for your given job, up through the level 70 quest. They serve as the starting tier relic weapons for Stormblood, and are upgraded in the Eureka zones. If you misplaced or discarded your Antiquated weapon, you can purchase a replacement for 1,000 from the Calamity Salvager in any of the three starting cities.
Note: If you can't find your Antiquated weapon and are not sure if you discarded it, you can type /isearch Antiquated to search for any Antiquated weapons across all of your inventory containers (Including bags, chocobo saddlebag, armoury, retainers, etc.).
Protean Crystals: Kill Notorious Monsters in The Forbidden Land, Eureka Anemos to earn Anemos Crystals, then turn them in to Gerolt to exchange for 2 to 5 Protean Crystals for each Anemos Crystal turned in. Protean crystals will also drop randomly from trash mobs of equal or higher elemental level to your own. In Eureka, a notorious monster is essentially a Kill Boss FATE.
Note that you must be on the matching job in order to augment your +2 weapon to an Anemos weapon, otherwise the menu option will not appear when speaking with Gerolt.
Frosted Protean Crystal: Collect vitiated aether by killing Notorious Monsters and level-appropriate trash mobs in Eureka Pagos, then turn it in at the Crystal Forge in Eureka Pagos (6.0, 21.5). You will receive one Frosted Protean Crystal for each full charge of vitiated aether.
You must have acquired the vitiated aether kettle from Gerolt by completing the level 25 quest in Eureka Pagos and obtaining at least one Anemos weapon before you can receive vitiated aether. However, you do not need to have the weapon of interest equipped to obtain vitiated aether.
The kettle can hold a maximum of 9 charges of vitiated aether. If it starts to get full, be sure to turn it in so none gets wasted!
Pagos Crystal: These are acquired by killing Notorious Monsters in Eureka Pagos. The higher level the Notorious Monster, the more crystals it will drop.
Louhi's Ice: 2 chunks will drop each time you complete the FATE Louhi on Ice with gold medal credit in Eureka Pagos, which requires you to kill the notorious monster Louhi. Louhi's Ice can also be purchased from the Expedition Birdwatcher for 50 Pagos Crystals each.
Pyros Crystal: These are acquired by killing Notorious Monsters in Eureka Pyros. The higher level the Notorious Monster, the more crystals it will drop.
An upgrade to Pyros weapons. Weapons will have a new model and swirling particle effects. This step grants the weapon's final appearance and maxes out its stats, excluding elemental stats that are effective in Eureka zones only. If you only care about the earning the glamour and don't care about the elemental stats, you can stop after completing this step.
Hydatos Crystal: These are acquired by killing Notorious Monsters in Eureka Hydatos. The higher level the Notorious Monster, the more crystals it will drop. While fewer crystals are needed compared to prior steps, Notorious Monsters in Hydatos also drop fewer crystals. A good source of crystals is the FATE The Baldesion Arsenal: Expedition Support, although this only spawns when there is an ongoing run of The Baldesion Arsenal.
Crystalline Scale: 3 scales will drop each time you complete the FATE Crystalline Provenance with gold medal credit in Eureka Hydatos, which requires you to kill the notorious monster Provenance Watcher. This is the only way to obtain the item as they are not sold by the Expedition Birdwatcher.
An upgrade to Eureka weapons. Stats and appearances are identical to Eureka weapons, except that they have extra Elemental Bonus stats that increase the weapons' power in Eureka zones only (including The Baldesion Arsenal).
Eureka Fragment: These are exclusively acquired inside The Baldesion Arsenal. A complete clear yields 28 fragments total, with each boss defeated dropping a portion of that total amount. It requires a total of four runs, assuming all of them are successful, to obtain enough fragments for one weapon.
Secondary Stats
An example roll with 5 "lines"
Eurekan Weapons at the Pyros, Eureka, or Physeos stages can have their secondary stats upgraded at the Mnemeworks Station, near Gerolt in Pyros. A weapon's secondary stats will be carried forward to any future item level upgrades. Intermediate-stage weapons in Hydatos (Hydatos, Hydatos +1, Base Eureka) cannot have their secondary stats modified.
These stats are rolled randomly, at the cost of 2 Smoldering Protean Crystals. Each weapon starts with one "line" of stats that it can randomly roll, and a total of 5 can be unlocked by repeatedly using the Mnemeworks Station. Each time the station is used, all unlocked lines reroll, and if 5 lines are not yet unlocked, there is a chance an additional line will be unlocked and rolled as well. The reroll can be canceled, leaving the weapon with its stats unmodified, but the 2 Smoldering Protean Crystals spent will not be refunded, and if the reroll unlocked an additional line the weapon will not retain it.
Paladin swords and shields are limited to 60, and 24 respectively.
The same stat can be randomly rolled on multiple lines. For example, if line 1 gives 48 Critical Hit, line 2 gives 30 Critical Hit, and line 3 gives 54 Skill Speed, the total stat bonuses are 78 Critical Hit and 54 Skill Speed.
Any stat bonuses totaling above 114 will be synced down to 114 inside of Eureka zones. These limits are 81 and 33 for paladin swords and shields, respectively. This means that bonuses larger than 114 will be partially "wasted".
There are 10 possible values for a given line, depending on the type of weapon:
Two-handed weapon
30
36
42
48
54
60
66
72
78
84
PLD sword
24
28
32
36
40
44
48
52
56
60
PLD shield
6
8
10
12
14
16
18
20
22
24
The available substats depend on the job the weapon is for:
Smoldering Protean Crystal: Collect vitiated aether by killing Notorious Monsters and level-appropriate trash mobs in Eureka Pyros, then turn it in at the Mark II Crystal Forge in Eureka Pyros (22.3, 6.0). You will receive one Smoldering Protean Crystal for each full charge of vitiated aether.
You must have acquired a Pyros Weapon before you can receive vitiated aether. You do not need to have the weapon equipped to obtain it.
The kettle can hold a maximum of 9 charges of vitiated aether. If it starts to get full, be sure to turn it in so none gets wasted!
Tips
Similar to materia melding, the most desirable substats to prioritize are generally: Critical Hit > Direct Hit Rate/Determination > Skill Speed/Spell Speed > Tenacity/Piety, although this varies depending on the job.
For example, a "perfect" roll for Melee DPS would be Critical Hit ≥ 114 (2 lines), Determination + 84, Direct Hit + 84, Skill Speed +84.
A good but not perfect roll could be Critical Hit ≥ 114 (2 lines), any Determination bonus (2 lines), any Direct Hit bonus (1 line).
Due to the random nature of substat rolls, achieving an optimal set of rolls can be very time-consuming. These substats are only useful for slightly increasing player power within Eureka zones, which is marginal compared to Elemental Bonus derived from Physeos Weapons, Elemental Armor +2, and Kirin's Osode Armor.
Eureka Weapon Types
Weapon Tier
IL
PLD
WAR
DRK
DRG
MNK
SAM
NIN
BRD
MCH
BLM
SMN
RDM
WHM
SCH
AST
Antiquated Starter
290
Starter
335
Starter +1
340
Starter +2
345
Anemos
355
Pagos
360
Pagos +1
365
Elemental
370
Elemental +1
375
Elemental +2
380
Pyros
385
Hydatos
390
Hydatos +1
395
Base Eureka
400
Eureka
405
Physeos
405
Gallery
Video presentation of all Eurekan weapons
Weapons can be viewed in these galleries. Individual galleries contain all stages of relic weapon for each job.
The Forbidden Land, Eureka.
Allagan Tomestones of Poetics.
1,000 from the Calamity Salvager in any of the three starting cities.
Stormblood. Additionally they need to complete the quest 
And We Shall Call it Eureka.
100
3
Protean Crystals: Kill Notorious Monsters in The Forbidden Land, Eureka Anemos to earn 
Anemos Crystals, then turn them in to Gerolt to exchange for 2 to 5 Protean Crystals for each Anemos Crystal turned in. Protean crystals will also drop randomly from trash mobs of equal or higher elemental level to your own. In Eureka, a notorious monster is essentially a Kill Boss FATE.
Pazuzu's Feathers: 3 feathers will drop each time you complete the FATE 
Wail in the Willows with gold medal credit in Eureka Anemos, which requires you to kill the notorious monster Pazuzu. Feathers can also be purchased from the Expedition Birdwatcher for 
5
500
5
Frosted Protean Crystal: Collect vitiated aether by killing Notorious Monsters and level-appropriate trash mobs in Eureka Pagos, then turn it in at the Crystal Forge in Eureka Pagos (6.0, 21.5). You will receive one 
Pagos Crystal: These are acquired by killing Notorious Monsters in Eureka Pagos. The higher level the Notorious Monster, the more crystals it will drop.
Louhi's Ice: 2 chunks will drop each time you complete the FATE 
150, must have unlocked 10 unique 
Logos Actions
5, must have unlocked 30 unique 
30
Pyros Crystal: These are acquired by killing Notorious Monsters in Eureka Pyros. The higher level the Notorious Monster, the more crystals it will drop.
Penthesilea's Flame: 3 chunks will drop each time you complete the FATE 
50
5
Hydatos Crystal: These are acquired by killing Notorious Monsters in Eureka Hydatos. The higher level the Notorious Monster, the more crystals it will drop. While fewer crystals are needed compared to prior steps, Notorious Monsters in Hydatos also drop fewer crystals. A good source of crystals is the FATE 
The Baldesion Arsenal.
Crystalline Scale: 3 scales will drop each time you complete the FATE 
100
Eureka Fragment: These are exclusively acquired inside 
Smoldering Protean Crystals. Each weapon starts with one "line" of stats that it can randomly roll, and a total of 5 can be unlocked by repeatedly using the Mnemeworks Station. Each time the station is used, all unlocked lines reroll, and if 5 lines are not yet unlocked, there is a chance an additional line will be unlocked and rolled as well. The reroll can be canceled, leaving the weapon with its stats unmodified, but the 2 
