Here is my report for primogem and fate income in May 2021 in order to help you better plan out your pulls!

Note that apart from F2P and Paid categories, I also included a third one called "Your-Millage-May-Vary (YMMV)". Gems in this category would still technically count as F2P, but depending on the player, it could either be hard to obtain (like Spiral Abyss or limited-quantity promo codes,) or yet to be obtained due to difference in progress (like time-gated content, non-quest-based achievements, or future world exploration.) Gems in this category are based on my personal progress.

Genesis Crystals from Welkin are excluded from the gem count since skins cost 1680 Genesis Crystals (before discount), and Welkin's buyers would most likely want to save their crystals for skins they might want now or in the future.

Pity calculations are using 82 soft pity (based on data from the Wish Tally project; most pities occur before 82.)

As usual, if you believe something is missing, or if you have any suggestions, please comment and let me know.

In case you're looking for past counts (posted on official r/Genshin_Impact subreddit):

April 2021

March 2021

February 2021

January 2021

November and December 2020 (courtesy of u/fffeeelll)

This Month's Summary:

Total F2P Event Banners:

29.54 to 40.86 wishes

avg. 0.95 to 1.32 wishes per day

4727 to 6538 primogems equivalent

36% to 50% pity

Total Paid Event Banners (including F2P):

55.23 to 66.55 wishes

avg. 1.78 to 2.15 wishes per day

8837 to 10648 primogems equivalent

67% to 81% pity

Verdict: This month is very similar to January, as it is entirely wrapped inside v1.5 (like January with v1.2) with no version update, and thus, no apologems. Half of Energy Amplifier Initiation's gems are also obtainable in April, making May the worst month yet since February (but still better than January with the addition of Serenitea Pot gems.)

F2P Primogems:

1860: Daily Commission

60 per day * 31

1640: Event

480: Energy Amplifier Initiation (990 total, 510 counted in April)

300: Event Shop (counted in April)

150: Act I (counted in April)

90: 30 per Place of Interest * 3

60: Domain: Vishap's Rest

150: Act II

90: 30 per Place of Interest * 3

60: Domain: Where Shadows Writhe

150: Act III

90: 30 per Place of Interest * 3

60: Domain: Frost-Worn Space

180: Twisted Realm:

60: Domain of Deceit (counted in April)

60: Domain of Furious Thunder

60: Domain of Chaos

60: Domain of Heresy

420: Windtrace

30 per 300 Windtrace Coins * 14 (up to 4200 Windtrace Coins)

20: Eula Test Run

420: Battlefront: Misty Dungeon

70 per Trial * 6

300: Mimi Tomo

60 per sighting * 5 (last 2 days are in June)

300: Promo Code

100: W***BYSZJNRD - Version 1.6 Special Program (expired)

100: 8A6ABHTH2N9Z - Version 1.6 Special Program (expired)

100: UTNBBGSZ3NQM - Version 1.6 Special Program (expired)

67: Quest

67: Aphros Delos Chapter: Act I - The Spindrift Shall Never Return to the Sea

60: completion

7: chest

60: HoYoLAB

60: Daily Check-In (20 * 3)

Total F2P earning so far: 3927 (24.54 wishes, 30% pity)

F2P Your-Millage-May-Vary Primogems:

1201: Spiral Abyss

50 per 3 Abyssal Stars * 0 to 36 stars * 2 rounds

1: Tutorial - Abyss Lector: Violet Lightning (entering Floor 12 Chamber 3 required)

360: Serenitea Pot Trust Rank

60 per Rank, from 5 to 10

200: Achievements

180: A Realm Beyond: Series I

5+10+20: High Adeptal Energy Readings Ahead (Reach 20,000 Adeptal Energy in 1/2/3 realm layouts.)

10+20: Friend of the Realm (Reach Trust Rank 7/10 with the teapot spirit.)

10+20: T—T—T—Timberhochwandi (Obtain 600/2,000 pieces of wood.)

5+10: If I Were a Rich Man (Obtain 2,000/10,000 realm currency.)

5+10: Not Just a Small Bench (Create 120/300 furnishings.)

5+10+20: Precision Modeling (Learn 60/120/180 furnishing blueprints.)

20: My... Territory (Place 300 furnishings in a single realm layout.)

20: Wonders of the World

20: Sternest of Souls (Defeat Azhdaha in all its forms.)

50: Promo Code (limited quantity)

Genshin Impact v1.5 50 Primogems Giveaway

Source 1: SEA** (ended)

Source 2: SteelSeries Games (still available as of writing)

Source 3: Crucial Games (still available as of writing)

Source 4: Intel® Gaming Access (still available as of writing)

Total F2P earning including YMMV: 5738 (35.86 wishes, 44% pity)

Paid Primogems:

2790: Blessing of the Welkin Moon

90 per day * 31

680: "Realm of Diversion" Battle Pass

Gnostic Hymn Lv. 50 reward

Total paid earning:

including F2P: 7397 (46.23 wishes, 56% pity)

including F2P+YMMV: 9208 (57.55 wishes, 70% pity)

Fates:

10: Acquaint

5: "Realm of Diversion" Battle Pass

5: Stardust Exchange (YMMV)

12% pity, equivalent to 1600 primogems

5 or 9: Intertwined

0 or 4: "Realm of Diversion" Battle Pass (paid Gnostic Hymn required)

5: Stardust Exchange (YMMV)

6% or 11% pity, equivalent to 800 or 1440 primogems

Additional Personal Stats. for Reference (Welkin+BP)

Primogems:

20: older achievements

4: exploration

310: crystals from welkin (This was a mistake. I should have saved it for skins...)

Personal total: 9542 primogems, 68.64 event pulls (equivalent to 10982 primogems, 84% pity)