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The seed "8255665205000737968" contains a cave system that is colossal even by 1.6.4 standards - except that this is for current (1.7 and later) versions:

Here is a zoomed-out view of a 1616x1616 block area; the cave system is centered right around the origin (0,0):

Here are some screenshots taken from inside the cave and with Spectator mode:

While the seed I used for this example is "8255665205000737968" many other seeds - a total of 65,536 - will also work thanks to a quirk in the code; here are AMIDST maps of 6 different seeds, including this one (the first map) - note the similarities between each seed; in particular, mineshafts are identical, including three just to the south of the cave system and even the shapes of some biomes and rivers are similar despite that part of world generation using the full 64 bit seed. The seed I used also has a taiga village around 515, -205 (not shown here):

Of note, the seed I originally discovered this cave system in is "8253976355140474032" but I did not include it because there is an ocean around 0,0; I just added 281474976710656 (2^48) to this seed until I found suitable seeds; I used the second one to generate the world due to the absence of oceans or swamps nearby, which would overwrite parts of the cave system (this works with any seed, allowing you to manipulate biome generation to your liking after finding a seed with good caves).

Also, I found this seed with a utility I wrote that searches through seeds for the densest concentrations of caves; this was the top result out of several million seeds searched. The cave system also has more than 300 individual caves and a volume of more than 370,000 air blocks:

This is an analysis from a utility I wrote that counts the number of air blocks within an area and outputs a list of the densest area(s) found, in this case within a circular radius of 8 chunks (213 chunks covered):

Seed is 8253976355140474032

Cave size is 15 and cave chance is 7
Ravine chance is 50 and version used is >= 1.7.2
Center of area to search is 0, 0
Area to search is from -64, -64 to 64, 64
Radius to calculate air volume over is 8 chunks
Altitude range is 11 to 62

Generating caves (may take a while)... 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Calculating air volume...
Creating list of densest regions found...
Removing redundant entries...
Sorting list...

Top 1 regions found by air volume between layers 11-62:
Air volume of 372390 (13.13%) at 24, 24

Here is an analysis from MCEdit of a 200W x 272L x 52H rectangular area centered over the cave system (212.5 chunks between y=11 and y=62):

Here is a list of all of the cave systems within a 17x17 chunk area centered on the cave system. Note that there are quite a few cave systems which match at oppositely-signed coordinate pairs, which is due to a bug within the code that calculates the per-chunk seed, giving the same results for those chunks; this also favors the generation of the largest cave systems right around the origin (the bug is by no means limited to the origin, it just means that a dense concentration of caves around a given coordinate may be mirrored at the oppositely-signed coordinate. Some seeds have as many as 1/3 of chunks being affected while a few appear to have none):

Seed is 8253976355140474032
Center is 0, 0 (chunk 0, 0)
Radius is 8 chunks (square)
Version used is >= 1.7.2

Size 1 cave system at -128, -112; total number of caves: 2
Size 3 cave system at -80, -112; total number of caves: 3
Size 1 cave system at -48, -112; total number of caves: 1
Size 7 cave system at 80, -112; total number of caves: 11
Size 1 cave system at -112, -80; total number of caves: 1
Size 4 cave system at -48, -80; total number of caves: 9
Size 11 cave system at -16, -80; total number of caves: 13
Size 8 cave system at 80, -80; total number of caves: 13
Size 3 cave system at -32, -64; total number of caves: 4
Size 7 cave system at 128, -64; total number of caves: 10
Size 1 cave system at -128, -48; total number of caves: 1
Size 12 cave system at -32, -48; total number of caves: 14
Size 7 cave system at 48, -48; total number of caves: 7
Size 6 cave system at -64, -32; total number of caves: 6
Size 5 cave system at -48, -32; total number of caves: 12
Size 3 cave system at -32, -32; total number of caves: 4
Size 3 cave system at 112, -32; total number of caves: 5
Size 1 cave system at -32, -16; total number of caves: 2
Size 11 cave system at -16, -16; total number of caves: 19
Size 1 cave system at -48, 0; total number of caves: 1
Size 1 cave system at 0, 0; total number of caves: 1
Size 6 cave system at 16, 0; total number of caves: 12
Size 1 cave system at 64, 0; total number of caves: 1
Size 7 cave system at 96, 0; total number of caves: 10
Size 11 cave system at 16, 16; total number of caves: 19
Size 4 cave system at -64, 32; total number of caves: 4
Size 1 cave system at -48, 32; total number of caves: 1
Size 3 cave system at 32, 32; total number of caves: 4
Size 2 cave system at 64, 32; total number of caves: 5
Size 1 cave system at -64, 48; total number of caves: 1
Size 7 cave system at -48, 48; total number of caves: 7
Size 11 cave system at 0, 64; total number of caves: 13
Size 8 cave system at 32, 64; total number of caves: 9
Size 8 cave system at -80, 80; total number of caves: 13
Size 11 cave system at 16, 80; total number of caves: 13
Size 4 cave system at 48, 80; total number of caves: 9
Size 1 cave system at 112, 80; total number of caves: 1
Size 2 cave system at -48, 96; total number of caves: 4
Size 1 cave system at 16, 96; total number of caves: 1
Size 7 cave system at -80, 112; total number of caves: 11
Size 3 cave system at 0, 112; total number of caves: 5
Size 1 cave system at 48, 112; total number of caves: 1
Size 3 cave system at 80, 112; total number of caves: 3
Size 1 cave system at -96, 128; total number of caves: 2
Size 7 cave system at 64, 128; total number of caves: 15
Size 2 cave system at 80, 128; total number of caves: 2

Number of cave systems: 46
Initial number of caves: 210
Total number of caves: 305
Additional circular room caves: 95
Number of small caves: 297; average width is 5.93
Number of large caves: 8; average width is 13.34
Number of circular rooms: 62; average width is 11.50
Additional caves per circular room: 1.53
Average caves per chunk: 1.0553633 (289 chunks)

Average altitude: 33.60
Percentage of caves on layers 0 to 9: 16.72
Percentage of caves on layers 10 to 19: 15.41
Percentage of caves on layers 20 to 29: 16.07
Percentage of caves on layers 30 to 39: 19.34
Percentage of caves on layers 40 to 49: 11.48
Percentage of caves on layers 50 to 59: 7.21
Percentage of caves above layer 59: 13.77

In addition, here is a comparison to a 1.6.4 seed; despite the larger cave systems in general there are only a couple areas across a much larger area that come close in terms of overall size:

The base seed is "4138077197488". That's the base 10 integer equal to the 48 bit number:
0000 0011 1100 0011 0111 1000 1001 1111 0001 0100 1011 0000 (spaces added to show that it's 12 groups of 4 bits).
Any 64 bit seed with the above pattern in the lower 48 bits will have the huge cave complex at 0,0.

Valid base 10 Minecraft seed input values are 64 bit signed integers. Therefore, as TheMasterCaver, stated there are 65,536 worlds with this underground characteristics.
That is, with the upper 16 bit of the 64 in the range of 0000 0000 0000 0000 thru 1111 1111 1111 1111 (0000 to FFFF hex).

So, if you want to use Amidst to search for a biome map that you like with this cave pattern start with "4138077197488" (map shown below) and start adding "281474976710656".

The next one in the series is "285613053908144", also shown below.

EDIT: To calculate the negative seeds start with "-9223367898777578320" and again start adding "281474976710656".

The negative seed closest to zero is "-277336899513168".

I use MicroSofts Calculator.exe in "Programmer" mode to toggle the upper bits off and on as desired so that I don't have to remember "281474976710656". See third image.

There are no dangerous weapons. There are only dangerous people. R.A. Heinlein
If you aren't part of the solution, then you obviously weren't properly dissolved.

The seed "8255665205000737968" contains a cave system that is colossal even by 1.6.4 standards - except that this is for current (1.7 and later) versions:

Here is a zoomed-out view of a 1616x1616 block area; the cave system is centered right around the origin (0,0):

Here are some screenshots taken from inside the cave and with Spectator mode:

While the seed I used for this example is "8255665205000737968" many other seeds - a total of 65,536 - will also work thanks to a quirk in the code; here are AMIDST maps of 6 different seeds, including this one (the first map) - note the similarities between each seed; in particular, mineshafts are identical, including three just to the south of the cave system and even the shapes of some biomes and rivers are similar despite that part of world generation using the full 64 bit seed. The seed I used also has a taiga village around 515, -205 (not shown here):

Of note, the seed I originally discovered this cave system in is "8253976355140474032" but I did not include it because there is an ocean around 0,0; I just added 281474976710656 (2^48) to this seed until I found suitable seeds; I used the second one to generate the world due to the absence of oceans or swamps nearby, which would overwrite parts of the cave system (this works with any seed, allowing you to manipulate biome generation to your liking after finding a seed with good caves).

Also, I found this seed with a utility I wrote that searches through seeds for the densest concentrations of caves; this was the top result out of several million seeds searched. The cave system also has more than 300 individual caves and a volume of more than 370,000 air blocks:

Seed is 8253976355140474032

Cave size is 15 and cave chance is 7

Ravine chance is 50 and version used is >= 1.7.2

Center of area to search is 0, 0

Area to search is from -64, -64 to 64, 64

Radius to calculate air volume over is 8 chunks

Altitude range is 11 to 62

Generating caves (may take a while)... 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Calculating air volume...

Creating list of densest regions found...

Removing redundant entries...

Sorting list...

Top 1 regions found by air volume between layers 11-62:

Air volume of 372390 (13.13%) at 24, 24

Here is an analysis from MCEdit of a 200W x 272L x 52H rectangular area centered over the cave system (212.5 chunks between y=11 and y=62):

Here is a list of all of the cave systems within a 17x17 chunk area centered on the cave system. Note that there are quite a few cave systems which match at oppositely-signed coordinate pairs, which is due to a bug within the code that calculates the per-chunk seed, giving the same results for those chunks; this also favors the generation of the largest cave systems right around the origin (the bug is by no means limited to the origin, it just means that a dense concentration of caves around a given coordinate may be mirrored at the oppositely-signed coordinate. Some seeds have as many as 1/3 of chunks being affected while a few appear to have none):

Seed is 8253976355140474032

Center is 0, 0 (chunk 0, 0)

Radius is 8 chunks (square)

Version used is >= 1.7.2

Size 1 cave system at -128, -112; total number of caves: 2

Size 3 cave system at -80, -112; total number of caves: 3

Size 1 cave system at -48, -112; total number of caves: 1

Size 7 cave system at 80, -112; total number of caves: 11

Size 1 cave system at -112, -80; total number of caves: 1

Size 4 cave system at -48, -80; total number of caves: 9

Size 11 cave system at -16, -80; total number of caves: 13

Size 8 cave system at 80, -80; total number of caves: 13

Size 3 cave system at -32, -64; total number of caves: 4

Size 7 cave system at 128, -64; total number of caves: 10

Size 1 cave system at -128, -48; total number of caves: 1

Size 12 cave system at -32, -48; total number of caves: 14

Size 7 cave system at 48, -48; total number of caves: 7

Size 6 cave system at -64, -32; total number of caves: 6

Size 5 cave system at -48, -32; total number of caves: 12

Size 3 cave system at -32, -32; total number of caves: 4

Size 3 cave system at 112, -32; total number of caves: 5

Size 1 cave system at -32, -16; total number of caves: 2

Size 11 cave system at -16, -16; total number of caves: 19

Size 1 cave system at -48, 0; total number of caves: 1

Size 1 cave system at 0, 0; total number of caves: 1

Size 6 cave system at 16, 0; total number of caves: 12

Size 1 cave system at 64, 0; total number of caves: 1

Size 7 cave system at 96, 0; total number of caves: 10

Size 11 cave system at 16, 16; total number of caves: 19

Size 4 cave system at -64, 32; total number of caves: 4

Size 1 cave system at -48, 32; total number of caves: 1

Size 3 cave system at 32, 32; total number of caves: 4

Size 2 cave system at 64, 32; total number of caves: 5

Size 1 cave system at -64, 48; total number of caves: 1

Size 7 cave system at -48, 48; total number of caves: 7

Size 11 cave system at 0, 64; total number of caves: 13

Size 8 cave system at 32, 64; total number of caves: 9

Size 8 cave system at -80, 80; total number of caves: 13

Size 11 cave system at 16, 80; total number of caves: 13

Size 4 cave system at 48, 80; total number of caves: 9

Size 1 cave system at 112, 80; total number of caves: 1

Size 2 cave system at -48, 96; total number of caves: 4

Size 1 cave system at 16, 96; total number of caves: 1

Size 7 cave system at -80, 112; total number of caves: 11

Size 3 cave system at 0, 112; total number of caves: 5

Size 1 cave system at 48, 112; total number of caves: 1

Size 3 cave system at 80, 112; total number of caves: 3

Size 1 cave system at -96, 128; total number of caves: 2

Size 7 cave system at 64, 128; total number of caves: 15

Size 2 cave system at 80, 128; total number of caves: 2

Number of cave systems: 46

Initial number of caves: 210

Total number of caves: 305

Additional circular room caves: 95

Number of small caves: 297; average width is 5.93

Number of large caves: 8; average width is 13.34

Number of circular rooms: 62; average width is 11.50

Additional caves per circular room: 1.53

Average caves per chunk: 1.0553633 (289 chunks)

Average altitude: 33.60

Percentage of caves on layers 0 to 9: 16.72

Percentage of caves on layers 10 to 19: 15.41

Percentage of caves on layers 20 to 29: 16.07

Percentage of caves on layers 30 to 39: 19.34

Percentage of caves on layers 40 to 49: 11.48

Percentage of caves on layers 50 to 59: 7.21

Percentage of caves above layer 59: 13.77

In addition, here is a comparison to a 1.6.4 seed; despite the larger cave systems in general there are only a couple areas across a much larger area that come close in terms of overall size:

TheMasterCaver's First World - possibly the most caved-out world in Minecraft history - includes world download.

TheMasterCaver's World - my flagship mod which combines my own ideas with 1.7+ features, with emphasis on underground content.

Why do I still play in 1.6.4?

The base seed is "4138077197488". That's the base 10 integer equal to the 48 bit number:

0000 0011 1100 0011 0111 1000 1001 1111 0001 0100 1011 0000 (spaces added to show that it's 12 groups of 4 bits).

Any 64 bit seed with the above pattern in the lower 48 bits will have the huge cave complex at 0,0.

Valid base 10 Minecraft seed input values are 64 bit signed integers. Therefore, as TheMasterCaver, stated there are 65,536 worlds with this underground characteristics.

That is, with the upper 16 bit of the 64 in the range of 0000 0000 0000 0000 thru 1111 1111 1111 1111 (0000 to FFFF hex).

So, if you want to use Amidst to search for a biome map that you like with this cave pattern start with "4138077197488" (map shown below) and start adding "281474976710656".

The next one in the series is "285613053908144", also shown below.

EDIT: To calculate the negative seeds start with "-9223367898777578320" and again start adding "281474976710656".

The negative seed closest to zero is "-277336899513168".

I use MicroSofts Calculator.exe in "Programmer" mode to toggle the upper bits off and on as desired so that I don't have to remember "281474976710656". See third image.

There are no dangerous weapons. There are only dangerous people. R.A. Heinlein

If you aren't part of the solution, then you obviously weren't properly dissolved.

If you have questions about the maps I post as attachments or Amidst and the like read this thread:

Using Amidst type programs to map and research Seeds

The latest release of Amidst, version 4.3-beta2 can be found here:

https://github.com/toolbox4minecraft/amidst/releases