How far do I have to place torches so that mobs will not spawn near me?

Since torches prevent mobs from spawning, is it possible to place enough torches within a specific radius to ensure safety during the night? I’m thinking of a situation without any shelter built, more along the lines of a flat plain. If it is possible, how many torches/how far out do I need to go to make that area safe?

• Sunlight gives 15 luminance to the blocks it hits directly, or through half steps.
• Lava gives 15 luminance.
• Glowstone gives 15 luminance.
• A Jack-o-lantern gives 15 luminance.
• A Torch gives 14 luminance to the otherwise empty block it occupies.
• A Redstone torch gives 7 luminance to the otherwise empty block it occupies.
• Every tile that isn’t a light source has a luminance of one minus the luminance of its neighbors. For example, if you had a 6 and a 4 luminance sources close to each other, attached to a wall, you’d have this distribution:

``````            1
121
1   12321
121 1234321
1232123454321
123432345654321
12┴─────┴4321
1     12321
121
1
``````

…except this works in three dimensions instead of two!

1. The following applies to any difficulty, except for Easy.
2. Every tile within 24 distance of the player is not eligible.
3. Every tile outside a 144×144 square centered on you is not eligible.
• Every non-glass, non-half step surface in the outer world with 7 or less luminance is eligible for spawning.
• Every non-glass, non-half step surface in the Nether is eligible for spawning.
4. Mob spawners cause mob to spawn at a high rate in any surface within 5 distance of it.
3. In practice:

Here’s what I try to do to ensure a luminance of 7 consistently along a line:

1. Place the first torch. Pardon my hexadecimal one-sided luminance graph:

``````EDCBA98765432100000000000000000
↑
``````
2. Proceed until you find two tiles looking exactly like the next, then go back one.

``````EDCBA98765432100000000000000000
↑
``````
3. Plant a torch there. Lo and behold, minimum luminance there will be 8!

``````EDCBA9889ABCDEDCBA98765432100
↑
``````
4. GOTO 1

You can adapt this algorithm to your necessities with ease. Just plant a torch in the darkest area when in doubt. (Duh.)

Also:

• Put torches directly onto surfaces for best results.
• In your mining, be aware that any surface is good enough to spawn…

``````↓↓↓ ↓↓    All positions marked with an arrow are valid
███ ██↓   spawning points, to the best of my knowledge,
█     █↓  and they all can lead to the just spawned mob
█      █  to reach you.
█     ↓█
█↓↓↓↓↓█   Be vigilant and don't mine caves from the
███████   bottom up :(
``````
4. Learn how to keep mob that has spawned outside: make traps.

• Mobs can only jump up one tile. Make pits deeper than that and, once in, they will be trapped (skeletons are still dangerous and spiders can climb out).
• Mobs cannot deconstruct. Make walls. (Be aware creepers do explode, if they get close enough.) Use cobblestone: they have high explosion resistance and can’t catch fire.
• Mobs cannot use items. Protect your entrance with a wooden door. Plant it from the outside, or skeletons will be able to hurt you with their arrows!
• Mobs’ path finding is somewhat dumb. Protect your spawn point with water and liberal amounts of cactus (arrange them in a chequered pattern.)