A349646 Nonnegative integers which produce a record maximum MD5 hash.

0, 3, 44, 65, 83, 373, 575, 1126, 12673, 25670, 30268, 30525, 40691, 48240964, 63327632, 298506737, 369490840, 1113434519, 1647703600, 4958115803, 64657664035, 86155378906, 184280298746, 400812644253, 411723964986, 714853066875, 1627993432495, 2607864795784

Offset: 1

Author

Ben Whitmore, Nov 23 2021

Keywords

• nonn
• base
• fini
• hard

Comments

a(1) = 0; a(n) is the smallest k such that MD5(k) > MD5(a(n-1)), where integer parameters to MD5 are encoded as base-10 ASCII strings.

If a(1) were defined as 1 instead of 0, the sequence would begin 1, 2, 3, 44, ... and then continue in the same way.

If we assume that MD5 behaves like a random function from N to {0, ..., 2^128-1}, the expected length of this sequence is the harmonic number H(2^128) ~= 89.3.

a(31) > 10^15.

Examples

			a(5) = 83 because MD5("83") = fe9fc289c3ff0af142b6d3bead98a923_16 = 338453431832254946862081270079334951203, which is larger than all previous values MD5("0"), ..., MD5("82").
		

Links

• Ben Whitmore, Table of n, a(n) for n = 1..30
• Wikipedia, MD5

Crossrefs

Record minima: A349647.

Programs

Mathematica

recordsBy[l_, P_] :=
Module[{max = -Infinity, x, i, recs = {}},
For[i = 1, i <= Length[l], i++,
  x = P[l[[i]]];
  If[x > max,
   max = x;
   AppendTo[recs, l[[i]]];
  ]
];
recs
];
recordsBy[Range[1000], Hash[ToString[#], "MD5"] &]

Python

from hashlib import md5
def afind(limit):
    record = ""
    for k in range(limit+1):
        hash = md5(str(k).encode('utf-8')).hexdigest()
        if hash > record:
            print(k, end=", ")
            record = hash
afind(10**5) # Michael S. Branicky, Nov 24 2021