starts-with is much slower than ends-with

[Quantum10101]

First I want to say thank you and good job on this much needed program!

I noticed that looking for 4 character keys using starts-with is much slower than looking for 4 character keys using ends-with. I tried this using both the latest commit 486d851 and also d4a7607 before support for multiple prefixes were added. I get the same issue, with starts-with taking much longer.

Here is an example to compare the two. Note that this same problem happens with other character combinations, not just "aaaa":

starts-with: 8 per minute
ends-with: 43 per minute

python3 main.py search-pubkey --starts-with aaaa --count 99999999 --output-dir ~/keygen/test

[INFO 2025-04-29 05:00:15,388] GPU 0 Speed: 16.22 MH/s
[INFO 2025-04-29 05:00:16,412] GPU 0 Speed: 16.41 MH/s
[INFO 2025-04-29 05:00:17,434] GPU 0 Speed: 16.43 MH/s
[INFO 2025-04-29 05:00:18,462] GPU 0 Speed: 16.32 MH/s
[INFO 2025-04-29 05:00:19,489] GPU 0 Speed: 16.34 MH/s
[INFO 2025-04-29 05:00:20,515] GPU 0 Speed: 16.38 MH/s
[INFO 2025-04-29 05:00:21,543] GPU 0 Speed: 16.32 MH/s
[INFO 2025-04-29 05:00:22,571] GPU 0 Speed: 16.33 MH/s
[INFO 2025-04-29 05:00:22,602] Found: aaaaz18tVZwXjP1yeeeTtBQSkBdcx7ax2KmNyPL8fp9
[INFO 2025-04-29 05:00:23,697] GPU 0 Speed: 16.44 MH/s
[INFO 2025-04-29 05:00:24,720] GPU 0 Speed: 16.42 MH/s
[INFO 2025-04-29 05:00:24,747] Found: aaaaFJUdBanQQm9ZecddeFHQydZH8vFFXKQ4YEhDVPR
[INFO 2025-04-29 05:00:25,852] GPU 0 Speed: 16.39 MH/s
[INFO 2025-04-29 05:00:26,886] GPU 0 Speed: 16.25 MH/s
[INFO 2025-04-29 05:00:26,910] Found: aaaawSjfHiY4gkmihcgBgbSNy8E7hgudkWVQTMynczh
[INFO 2025-04-29 05:00:28,012] GPU 0 Speed: 16.36 MH/s
[INFO 2025-04-29 05:00:28,038] Found: aaaanZRBhUjKM54jyd4fVz7doNJdSSSikGiYU2T1TrW
[INFO 2025-04-29 05:00:29,135] GPU 0 Speed: 16.43 MH/s
[INFO 2025-04-29 05:00:30,165] GPU 0 Speed: 16.30 MH/s
[INFO 2025-04-29 05:00:31,194] GPU 0 Speed: 16.31 MH/s
[INFO 2025-04-29 05:00:32,222] GPU 0 Speed: 16.33 MH/s
[INFO 2025-04-29 05:00:33,251] GPU 0 Speed: 16.32 MH/s
[INFO 2025-04-29 05:00:34,277] GPU 0 Speed: 16.36 MH/s
[INFO 2025-04-29 05:00:35,303] GPU 0 Speed: 16.36 MH/s
[INFO 2025-04-29 05:00:36,333] GPU 0 Speed: 16.31 MH/s
[INFO 2025-04-29 05:00:37,369] GPU 0 Speed: 16.21 MH/s
[INFO 2025-04-29 05:00:38,400] GPU 0 Speed: 16.28 MH/s
[INFO 2025-04-29 05:00:39,434] GPU 0 Speed: 16.24 MH/s
[INFO 2025-04-29 05:00:40,468] GPU 0 Speed: 16.24 MH/s
[INFO 2025-04-29 05:00:41,501] GPU 0 Speed: 16.25 MH/s
[INFO 2025-04-29 05:00:42,526] GPU 0 Speed: 16.37 MH/s
[INFO 2025-04-29 05:00:43,562] GPU 0 Speed: 16.20 MH/s
[INFO 2025-04-29 05:00:44,601] GPU 0 Speed: 16.17 MH/s
[INFO 2025-04-29 05:00:45,636] GPU 0 Speed: 16.21 MH/s
[INFO 2025-04-29 05:00:46,668] GPU 0 Speed: 16.28 MH/s
[INFO 2025-04-29 05:00:47,700] GPU 0 Speed: 16.26 MH/s
[INFO 2025-04-29 05:00:48,737] GPU 0 Speed: 16.19 MH/s
[INFO 2025-04-29 05:00:49,770] GPU 0 Speed: 16.24 MH/s
[INFO 2025-04-29 05:00:50,806] GPU 0 Speed: 16.21 MH/s
[INFO 2025-04-29 05:00:51,846] GPU 0 Speed: 16.14 MH/s
[INFO 2025-04-29 05:00:52,884] GPU 0 Speed: 16.17 MH/s
[INFO 2025-04-29 05:00:53,914] GPU 0 Speed: 16.29 MH/s
[INFO 2025-04-29 05:00:54,952] GPU 0 Speed: 16.18 MH/s
[INFO 2025-04-29 05:00:55,988] GPU 0 Speed: 16.20 MH/s
[INFO 2025-04-29 05:00:57,020] GPU 0 Speed: 16.27 MH/s
[INFO 2025-04-29 05:00:57,043] Found: aaaaNMjQMkRrNi1m46UDuukTBXy8YgxAm4pQk5Kz9eo
[INFO 2025-04-29 05:00:58,152] GPU 0 Speed: 16.26 MH/s
[INFO 2025-04-29 05:00:59,194] GPU 0 Speed: 16.13 MH/s
[INFO 2025-04-29 05:00:59,217] Found: aaaau2eP3LGe1AQ6iJ5zQELQGJ6FRjzfC1rEg37dBKm
[INFO 2025-04-29 05:01:00,334] GPU 0 Speed: 16.18 MH/s
[INFO 2025-04-29 05:01:01,375] GPU 0 Speed: 16.13 MH/s
[INFO 2025-04-29 05:01:02,408] GPU 0 Speed: 16.26 MH/s
[INFO 2025-04-29 05:01:03,448] GPU 0 Speed: 16.14 MH/s
[INFO 2025-04-29 05:01:03,472] Found: aaaazZWRSrW7JZ9FD38L845BGVpNF2km97VRgPNjxAh
[INFO 2025-04-29 05:01:04,588] GPU 0 Speed: 16.26 MH/s
[INFO 2025-04-29 05:01:05,631] GPU 0 Speed: 16.12 MH/s
[INFO 2025-04-29 05:01:05,655] Found: aaaaVXBNwUqCi7umg7Ly5j6RZTaiqT4TeBz24f2qSnS
[INFO 2025-04-29 05:01:06,851] GPU 0 Speed: 16.19 MH/s
[INFO 2025-04-29 05:01:07,885] GPU 0 Speed: 16.25 MH/s
[INFO 2025-04-29 05:01:08,913] GPU 0 Speed: 16.33 MH/s
[INFO 2025-04-29 05:01:09,967] GPU 0 Speed: 15.93 MH/s
[INFO 2025-04-29 05:01:11,007] GPU 0 Speed: 16.13 MH/s
[INFO 2025-04-29 05:01:12,041] GPU 0 Speed: 16.25 MH/s
[INFO 2025-04-29 05:01:13,105] GPU 0 Speed: 15.77 MH/s
[INFO 2025-04-29 05:01:14,151] GPU 0 Speed: 16.05 MH/s
[INFO 2025-04-29 05:01:15,194] GPU 0 Speed: 16.11 MH/s

python3 main.py search-pubkey --ends-with aaaa --count 99999999 --output-dir ~/keygen/test

[INFO 2025-04-29 05:02:41,265] GPU 0 Speed: 16.18 MH/s
[INFO 2025-04-29 05:02:42,290] GPU 0 Speed: 16.39 MH/s
[INFO 2025-04-29 05:02:42,332] Found: HfBkkehtVkkMtJCHXW6nU3hoMVA7Gpuc3gXA3Jmqaaaa
[INFO 2025-04-29 05:02:43,442] GPU 0 Speed: 16.42 MH/s
[INFO 2025-04-29 05:02:44,468] GPU 0 Speed: 16.36 MH/s
[INFO 2025-04-29 05:02:45,493] GPU 0 Speed: 16.39 MH/s
[INFO 2025-04-29 05:02:45,516] Found: 6mQ7T2KGiSEpnoci2TsKfqhcUMJtkFEieyDBLkb4aaaa
[INFO 2025-04-29 05:02:46,627] GPU 0 Speed: 16.35 MH/s
[INFO 2025-04-29 05:02:46,653] Found: vvCY88eghBp6fytKHEf95LRvUzJ4bjTkRfdeabzaaaa
[INFO 2025-04-29 05:02:47,755] GPU 0 Speed: 16.31 MH/s
[INFO 2025-04-29 05:02:48,777] GPU 0 Speed: 16.43 MH/s
[INFO 2025-04-29 05:02:49,798] GPU 0 Speed: 16.44 MH/s
[INFO 2025-04-29 05:02:49,825] Found: Bo28Rqy4Q4zNrF3qhc9VRZf5khr2vpUNvdpkBomBaaaa
[INFO 2025-04-29 05:02:50,931] GPU 0 Speed: 16.40 MH/s
[INFO 2025-04-29 05:02:50,956] Found: 7vywaid61ajzu8AULmL2bN45sPS7U2SurKGzJvYoaaaa
[INFO 2025-04-29 05:02:52,058] GPU 0 Speed: 16.49 MH/s
[INFO 2025-04-29 05:02:52,083] Found: CUapkwYyYfP3auWQCiCfaqYWvkrG9c8dGm2tB5jiaaaa
[INFO 2025-04-29 05:02:53,180] GPU 0 Speed: 16.46 MH/s
[INFO 2025-04-29 05:02:54,205] GPU 0 Speed: 16.39 MH/s
[INFO 2025-04-29 05:02:55,234] GPU 0 Speed: 16.32 MH/s
[INFO 2025-04-29 05:02:55,262] Found: 6THixux63cBm1hjpEMRGj5DTMHJLsYePACgpVCFLaaaa
[INFO 2025-04-29 05:02:56,371] GPU 0 Speed: 16.25 MH/s
[INFO 2025-04-29 05:02:56,396] Found: AeQRPe93Err4swMWyKCAsPVFcRihgy2mYCr1xE6Gaaaa
[INFO 2025-04-29 05:02:57,504] GPU 0 Speed: 16.38 MH/s
[INFO 2025-04-29 05:02:57,529] Found: AG85wt7QJtuTnQqdWZkPFA9UzqeX4XpfKiSSXYjTaaaa
[INFO 2025-04-29 05:02:58,629] GPU 0 Speed: 16.36 MH/s
[INFO 2025-04-29 05:02:58,654] Found: 4NwtjeGGNfq4eVHQgT74QreVabFKTtWQRR4qkkvzaaaa
[INFO 2025-04-29 05:02:59,799] GPU 0 Speed: 16.47 MH/s
[INFO 2025-04-29 05:03:00,835] GPU 0 Speed: 16.21 MH/s
[INFO 2025-04-29 05:03:00,860] Found: Fya2dMdhbec7mYgyXGcPa4LPcthDhuN9MCtwzWmuaaaa
[INFO 2025-04-29 05:03:01,962] GPU 0 Speed: 16.35 MH/s
[INFO 2025-04-29 05:03:01,989] Found: Bz4dENTfXf5eWnvEHGsQzkUq4VHtLQ7LksPSvCUWaaaa
[INFO 2025-04-29 05:03:03,152] GPU 0 Speed: 16.26 MH/s
[INFO 2025-04-29 05:03:03,180] Found: 8PUMb9zxyX38rJnp8aP2YEH81ivAsbEEz6vCLpdSaaaa
[INFO 2025-04-29 05:03:04,281] GPU 0 Speed: 16.43 MH/s
[INFO 2025-04-29 05:03:05,310] GPU 0 Speed: 16.32 MH/s
[INFO 2025-04-29 05:03:05,334] Found: 9Sk3ijaouwZbAxgauiUS7UkPw7wgWCchDSEgdwTQaaaa
[INFO 2025-04-29 05:03:06,430] GPU 0 Speed: 16.34 MH/s
[INFO 2025-04-29 05:03:06,455] Found: AqZfho8imD9CmU2G1Kqpwi2TZgYYF57H4iujJeZKaaaa
[INFO 2025-04-29 05:03:07,566] GPU 0 Speed: 16.30 MH/s
[INFO 2025-04-29 05:03:08,598] GPU 0 Speed: 16.28 MH/s
[INFO 2025-04-29 05:03:08,624] Found: 3Tqk5c2coA9aeZaA9BsVrXuKpLd49d9CpJQmxc8Gaaaa
[INFO 2025-04-29 05:03:09,717] GPU 0 Speed: 16.44 MH/s
[INFO 2025-04-29 05:03:09,744] Found: 8abkCzM53e4NxG3Kp95DPMmhKiGYcLwPaRNySRU5aaaa
[INFO 2025-04-29 05:03:10,849] GPU 0 Speed: 16.33 MH/s
[INFO 2025-04-29 05:03:10,874] Found: EcupWveG1yXFiv3DJ2S5ySBGtZQDnvq2sfadM6fUaaaa
[INFO 2025-04-29 05:03:12,011] GPU 0 Speed: 15.89 MH/s
[INFO 2025-04-29 05:03:12,037] Found: EAQNfBKAgC455DSVbDrzLNZBdcRzKYTfYJxFaD6Baaaa
[INFO 2025-04-29 05:03:13,166] GPU 0 Speed: 15.97 MH/s
[INFO 2025-04-29 05:03:13,190] Found: 2UDdov4ypLVABQdHLJGvHDkrzfVDHrNU7AR8HhxWaaaa
[INFO 2025-04-29 05:03:14,294] GPU 0 Speed: 16.40 MH/s
[INFO 2025-04-29 05:03:14,321] Found: HyBnQar8VEjAKpBez7oT8JQfRP5RS33nm8UgKZR8aaaa
[INFO 2025-04-29 05:03:15,418] GPU 0 Speed: 16.42 MH/s
[INFO 2025-04-29 05:03:15,443] Found: EKCUyJxN3v5vdaFgphDeF5A5sn9bp45aNZDrjE5Jaaaa
[INFO 2025-04-29 05:03:16,543] GPU 0 Speed: 16.37 MH/s
[INFO 2025-04-29 05:03:16,567] Found: kjHZSBPr6U1QnT3RocYYVciRA7V9ft9b3fExpWhaaaa
[INFO 2025-04-29 05:03:17,721] GPU 0 Speed: 16.30 MH/s
[INFO 2025-04-29 05:03:17,746] Found: CbmPjV6uwAGewugHeuCpffWi9PEpvbQL9NUz2Xjeaaaa
[INFO 2025-04-29 05:03:18,847] GPU 0 Speed: 16.28 MH/s
[INFO 2025-04-29 05:03:18,872] Found: 6YJeDYWD2uF7s6ZFuGJhueHmD27RrX9pCPqc3Y7Zaaaa
[INFO 2025-04-29 05:03:19,981] GPU 0 Speed: 16.31 MH/s
[INFO 2025-04-29 05:03:20,006] Found: A7msZYrFzWA6b2kxeVBtb3re88oo8WxmxBa1FvsKaaaa
[INFO 2025-04-29 05:03:21,106] GPU 0 Speed: 16.32 MH/s
[INFO 2025-04-29 05:03:22,137] GPU 0 Speed: 16.29 MH/s
[INFO 2025-04-29 05:03:22,167] Found: DHF8zvb6RsNtGnyoS8xpQJTATiLUcqhGrJcQXUwDaaaa
[INFO 2025-04-29 05:03:23,273] GPU 0 Speed: 16.36 MH/s
[INFO 2025-04-29 05:03:23,299] Found: ADvmpL31GGbEvvXeYPZwk3Sxq9AuBEQKcVFnaiMbaaaa
[INFO 2025-04-29 05:03:24,419] GPU 0 Speed: 16.29 MH/s
[INFO 2025-04-29 05:03:24,443] Found: 3kDnLx8voF2MnLYhzTthseTRN7HeLVrnL8YSa1gTaaaa
[INFO 2025-04-29 05:03:25,556] GPU 0 Speed: 16.30 MH/s
[INFO 2025-04-29 05:03:25,608] Found: 8hN8zthT9sHHNithBpiFRHPmtsNGJMRoZJQMokzuaaaa
[INFO 2025-04-29 05:03:26,720] GPU 0 Speed: 16.28 MH/s
[INFO 2025-04-29 05:03:26,745] Found: EXUXFbNLVvpbxVNKPSzRoyZFiUjmrLxZeQBTKFVRaaaa
[INFO 2025-04-29 05:03:27,844] GPU 0 Speed: 16.33 MH/s
[INFO 2025-04-29 05:03:27,868] Found: HX3m6cYtxaJkeVwvSxL4mq96gRYEQaN9xf35EANcaaaa
[INFO 2025-04-29 05:03:28,982] GPU 0 Speed: 16.18 MH/s
[INFO 2025-04-29 05:03:29,007] Found: 5TssLxKgBZqKyVWu1QdvDuyLuHPNagUjbjgdgbWaaaa
[INFO 2025-04-29 05:03:30,125] GPU 0 Speed: 16.23 MH/s
[INFO 2025-04-29 05:03:30,149] Found: 2Xexb8jhPuphB4dyFvPTMLYqf2jEp2EiUhuwFT6haaaa
[INFO 2025-04-29 05:03:31,269] GPU 0 Speed: 16.16 MH/s
[INFO 2025-04-29 05:03:31,297] Found: A6oh127pjjZRyVzBCB7EUzzA8R3KhcdBPNEs2HdBaaaa
[INFO 2025-04-29 05:03:32,402] GPU 0 Speed: 16.27 MH/s
[INFO 2025-04-29 05:03:32,426] Found: Cvr9CwVr9Vizsu8osKGhkgQUUDzukjHemo5qt2SUaaaa
[INFO 2025-04-29 05:03:33,548] GPU 0 Speed: 16.12 MH/s
[INFO 2025-04-29 05:03:33,574] Found: 8yRbbbQz7epw7kAkuuRtCck1QuNQ1aBYg9E8qGZuaaaa
[INFO 2025-04-29 05:03:34,681] GPU 0 Speed: 16.22 MH/s
[INFO 2025-04-29 05:03:34,705] Found: C1rqW9dsmDicJLUjw4sdN2qSjR6s62FtCNo7f38daaaa
[INFO 2025-04-29 05:03:35,820] GPU 0 Speed: 16.15 MH/s
[INFO 2025-04-29 05:03:35,844] Found: 98kTjq4MddkDGjcwNcjrAtgoWd1cd8BWVWWANn72aaaa
[INFO 2025-04-29 05:03:36,964] GPU 0 Speed: 16.22 MH/s
[INFO 2025-04-29 05:03:36,989] Found: 34ZDNrQgujWFv8JD1NGpUZbCgwgxqLdHNdce5cV4aaaa
[INFO 2025-04-29 05:03:38,147] GPU 0 Speed: 16.21 MH/s
[INFO 2025-04-29 05:03:38,175] Found: EBi8zwUWLsLswbnBZYZYW3dTHyDvSwpBsg2hsG7waaaa
[INFO 2025-04-29 05:03:39,289] GPU 0 Speed: 16.18 MH/s
[INFO 2025-04-29 05:03:40,329] GPU 0 Speed: 16.15 MH/s
[INFO 2025-04-29 05:03:40,355] Found: 3ddR6NQuXx9i6vnhAdC3ycAuSGrgxwbEdpTxhXf9aaaa
[INFO 2025-04-29 05:03:41,464] GPU 0 Speed: 16.24 MH/s
[INFO 2025-04-29 05:03:41,489] Found: CbZcykBMgJD5Ra1CbXNGEnni2xd2Pnvf8BPZgvSraaaa

Any idea why there would be such a difference?

[WincerChan]

Hello,
I’ve tried using “aaaa” as both a prefix and a suffix, and I obtained results similar to yours. However, I don’t think it’s a bug in the code. It’s caused by the algorithm.

Solana’s process is more complex: its 512-bit private key is derived from a seed using SHA-512, with only the first half used for key generation. Due to this hashing step, even if Solana’s private keys are incremented consecutively, the public keys remain non-sequential and appear more unpredictable than Ethereum’s.

Using a random string like “Gxkq” might yield different test results.

[Quantum10101]

No, I don't think it's the algorithm. I just ran the official Solana keygen grind program for a few hours:
solana-keygen grind --starts-with aaaa:99999999 --ends-with aaaa:99999999

It produced both of them at a practically identical rate:
"aaaa......" (29 times)
"......aaaa" (27 times)

The aaaa prefix and the aaaa suffix are produced by Solana's algorithm at the same rate, so if you are using the same algorithm, something else must be causing the prefix to be a lot slower here.

[WincerChan]

@Quantum10101 Oh, that’s interesting. I’ll look into it further.

[WincerChan]

Hello, I spent a lot of time investigating this issue, and now I’d like to share my findings. The base58 encoding method is the root cause of the difference in difficulty between prefixes and suffixes, and it only affects the first character (excluding ‘1’ as the first character).

First of all, here are all the characters in base58 encoding:

123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz

The following test code runs two million times to simulate random ed25519 key‐pair generation:

import secrets, collections
from nacl.bindings import crypto_sign_seed_keypair
import base58

counter_starts = collections.Counter()
counter_seconds = collections.Counter()
counter_both    = collections.Counter()
counter_ends    = collections.Counter()

for _ in range(2_000_000):
    seed  = secrets.token_bytes(32)
    pk, _ = crypto_sign_seed_keypair(seed)
    addr  = base58.b58encode(pk).decode()
    counter_starts[addr[0]]  += 1
    counter_seconds[addr[1]] += 1
    counter_ends[addr[-1]]   += 1
    if addr[0] == addr[1]:
        counter_both[f'{addr[0]}{addr[1]}'] += 1

Here are the results for how often each character appears as the first and second character:

Character set	First	First + Second
2–8, 9, A–H	115,832	1,947
J	28380	30
1	8,000	30
K–Z, a–z	2,087	28

Characters 2 through H appear as the first character over 55 × more often than those in K–z. Searching for a prefix whose first character is between 2 and H is therefore much easier; prefixes starting with K–z are significantly harder.

If you search for prefixes composed of many ‘1’s (e.g. 1111 or 11111), those are the hardest to find among all prefixes.

By contrast, every character appears 34,500 times in the last position.

I also tested with solana-keygen using aaaa as both prefix and suffix:

• ends aaaa: searched 755,000,000 keypairs in 4,174 s — 7 matches found
• starts aaaa: searched 755,000,000 keypairs in 4,176 s — 4 matches found

I reviewed the Solana CLI code and confirmed there is only one pruning filter applied after the public key is generated. That filter should not cause prefixes and suffixes to have the same match probabilities.

[Quantum10101]

Wow, that is very interesting and kind of mysterious. That's great testing!

We should note that at such a small sample size, 7 and 4 are not statistically very different. My test above was starts with aaaa 29 times and ends with aaaa 27 times with solana-keygen. I'll give it another try sometime soon.

[Quantum10101]

I don't know if this helps, but I thought of trying this with just 2 "aa" for start and 2 "aa" for end with solana-keygen. I get a very close number for both:

$ solana-keygen grind --starts-with aa:99999999
Searching with 8 threads for:
99999999 pubkeys that start with 'aa' and end with ''
Wrote keypair to aareKxXQpAFcELxsQCnSR73dUfk7YiYguF7jtmjJWdU.json
Wrote keypair to aaAaRNAzvznydK5PKpCearhzLa4Eo4wP1WooYN6RtGz.json
...
...
...
Wrote keypair to aahcjg7oBMaRc2TJatKKrmNfPKu98g7mhZY3X8eRKio.json
Wrote keypair to aacJ77um1y72aySHDnh6PSB7pDdakC2yg6VrPUmMur1.json
Searched 50000000 keypairs in 344s. 814 matches found.

$ solana-keygen grind --ends-with aa:99999999
Searching with 8 threads for:
99999999 pubkeys that start with '' and end with 'aa'
Wrote keypair to 9fVR5zV9yNpz85ueacmHUPNq2JJeusq3XpcM9v3zGaa.json
Wrote keypair to KN8ZwkNJjm2z5ruvSfMGD5mTwR3Hns1iZDJVv1nataa.json
...
...
...
Wrote keypair to Qiom3U8CA2aPQdJJLiA9ku2MMGHeFLBLPnH7gamLvaa.json
Wrote keypair to FMe67qdiiVKBbxfiuMranirAzubTqnnqZN5nAxvAeaa.json
Searched 50000000 keypairs in 342s. 892 matches found.

I think solana-keygen does cause prefixes and suffixes to have very close to the same match probabilities?

[5m1Ly]

My Conclusion, start with the character "1" and you'll speed up the process of finding your desired key.