How Many Bitcoin Seed Phrases Are Only One Repeated Word?

A reader wrote in via nostr:

There are 12 and 24 word seed phrases with reoccurring words. Bacon repeated 24 times is probably the most famous. Do you have a list of other words that reoccur 12 or 24 times?

Indeed, I stumbled across the "bacon" seed phrase back in 2018 though I haven't looked for others, so this is a neat question!

I wrote this script to iterate through every word in the BIP39 word list and check to see if a 12 or 24 word seed phrase with only that word repeated would be valid. To be clear, the BIP39 specification allows for generation of seed phrases that consist of 3 / 6 / 9 / 12 / 15 / 18 / 21 / 24 words, but for brevity I'll stick to the most commonly used 12 and 24 word lengths.

It turns out there are 130 valid seed phrases that are the same word repeated 12 times:

action x12
agent x12
aim x12
all x12
ankle x12
announce x12
audit x12
awesome x12
beef x12
believe x12
blue x12
border x12
brand x12
breeze x12
bus x12
business x12
cannon x12
canyon x12
carry x12
cave x12
century x12
cereal x12
chronic x12
coast x12
convince x12
cute x12
dawn x12
dilemma x12
divorce x12
dry x12
elevator x12
else x12
embrace x12
enroll x12
escape x12
evolve x12
exclude x12
excuse x12
exercise x12
expire x12
fetch x12
fever x12
forward x12
fury x12
garment x12
gauge x12
gym x12
half x12
harsh x12
hole x12
hybrid x12
illegal x12
include x12
index x12
into x12
invest x12
involve x12
jeans x12
kick x12
kite x12
later x12
layer x12
legend x12
life x12
lyrics x12
margin x12
melody x12
mom x12
more x12
morning x12
nation x12
neck x12
neglect x12
never x12
noble x12
novel x12
obvious x12
ocean x12
oil x12
orphan x12
oxygen x12
pause x12
peasant x12
permit x12
piano x12
proof x12
pumpkin x12
question x12
real x12
report x12
rough x12
rude x12
salad x12
scale x12
screen x12
sea x12
seat x12
sell x12
seminar x12
seven x12
sheriff x12
siege x12
silver x12
soldier x12
spell x12
split x12
spray x12
stadium x12
sugar x12
sunny x12
sure x12
tobacco x12
tongue x12
track x12
tree x12
trouble x12
twelve x12
twice x12
type x12
uniform x12
useless x12
valid x12
very x12
vibrant x12
virtual x12
vocal x12
warrior x12
word x12
world x12
yellow x12

However, there are only 11 valid seed phrases that are the same word repeated 24 times!

bacon x24
flag x24
gas x24
great x24
slice x24
solution x24
summer x24
they x24
trade x24
trap x24
zebra x24

Security Warning

In case it's not obvious, it would be a very bad idea to actually use any of the above seed phrases. In fact, I checked and several of them have been previously used! But of course, they're all empty - I'd be willing to bet that if you deposited any money into the above phrases at a standard derivation path, the funds would get swept within a minute or so. This is because there are folks out there running scripts that have generated billions of common seed phrases and brain wallets, just waiting for any unsuspecting person to deposit money into them.

Why the Discrepancy in Repetitive Counts?

The difference in the number of valid repeated 12-word and 24-word Bitcoin BIP39 mnemonics stems from the structure and requirements of the BIP39 standard, which involves a combination of entropy, checksum, and the mnemonic's word count.

Entropy and Checksum:

• 12-word mnemonic: Uses 128 bits of entropy and includes 4 bits of checksum. This results in 132 bits total, which are represented by 12 words.
• 24-word mnemonic: Uses 256 bits of entropy and includes 8 bits of checksum. This results in 264 bits total, represented by 24 words.
• For a mnemonic to be valid, its checksum must match the calculated checksum derived from the entropy. This means that only specific combinations of words will form a valid mnemonic. But there's always more than one valid checksum!

Why More Valid 12-Word Repeated Mnemonics Exist:

In a 12-word mnemonic, a smaller proportion of the mnemonic is devoted to the checksum (4 bits out of 132) compared to a 24-word mnemonic (8 bits out of 264). This means there are relatively more possible entropy configurations that could collide with a valid checksum for a given word when repeated.

Probability of Valid Checksum:

• 12-word repeats: With fewer bits in the checksum, the likelihood of randomly hitting a valid checksum is higher. More concretely: each 11 word partial seed phrase has 128 possible valid 12th words. As such, the probability that a given word, if repeated 11 times, will have a matching checksum is 6.25%.
• 24-word repeats: With more bits in the checksum, the precision required to match the correct checksum is higher. Therefore, the probability of a valid checksum occurring with a repeated word in all 24 positions is lower. More concretely: each 23 word partial seed phrase has 8 possible valid 24 words. As such, the probability that a given word, if repeated 23 times, will have a matching checksum is 0.39%.

A Practical Demonstration:

Let's say we have a partial seed phrase of "proof" repeated 11 times and we want to determine all valid checksums. Any of these 128 words will be valid as the 12th word.

absurd
addict 
afford 
always 
antique 
armed
arrive 
atom 
awful 
barrel 
betray 
blame 
bomb 
bounce 
bronze 
buzz 
canyon 
car 
certain 
chat 
choose 
climb 
coin 
come 
coyote 
crop 
cupboard 
dance 
decide
depend 
detail 
disease 
divorce 
drum 
earth 
egg 
else 
enlist 
equip 
exercise 
expand 
family 
festival 
finish 
flip 
focus 
frost 
future 
gentle 
glad 
goddess 
gravity 
hawk 
hint 
honey 
humor
impose 
index 
interest 
jazz 
jump 
kind 
labor 
lecture 
letter 
live 
lunch 
man 
master 
message 
miss 
modify 
mountain 
need 
nerve 
number 
object 
omit 
order 
panther 
peace 
pelican 
pipe 
play 
pottery 
price 
proof 
pyramid 
quote 
raven 
reject 
render 
rib 
riot 
round 
sample 
scale 
seek 
shallow 
ship 
six 
skill 
slow 
soul 
special 
sport 
stay 
subject 
success 
surround 
tail 
team 
thing
tilt 
tool 
traffic 
truck 
twelve 
unaware 
update 
vanish 
verify 
village 
wagon 
wear 
wild 
winter 
zoo

On the other hand, if we have a partial seed phrase of "bacon" repeated 23 times and we want to determine all valid checksums, the possible valid 24th word could only be one of the following:

bacon
cupboard
double
jelly
neutral
review
smile
voice

Conclusion

Because of the proportional differences in entropy and checksum between 12-word and 24-word mnemonics, there are statistically more valid configurations of the entropy for repeated 12-word phrases compared to 24-word phrases. This difference leads to a far higher number of valid repeated 12-word mnemonics than 24-word ones.