Biggest number challenge (Brainfuck)

Question

This is a brainfuck version of Largest Number Printable, and this.

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Let's think about brainfuck interpreter such that,

1. Has array that can be stretched left & right arbitrary large
2. Each cell can contain arbitrary large integer
   • Can contain negative integer too
3. When the interpreter starts, every cell is intialized by 0
4. . prints integer representation of value of cell, then LF.

For example, <<+++.>--. prints

3
-2

, then terminate.

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Description

Your goal is to write a brainfuck program that prints a number/numbers. The bigger the number, the more points you'll get.

There are some rules to follow.

• Your program must terminate.
• You should not use ,.
• You can print multiple integers.
• Your score will be largest number that the program prints.
• Maximum code length is 1024 bytes. (Only []+-><. counts)

Here is sample brainfuck interpreter that you could test.

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Leaderboards

:)

Answer 1

Score: 2↑↑45306

Edit: Replaced it with a more modifiable version. Try 2↑↑2, 2↑↑3, and 2↑↑4 (2↑↑5 times out)

Just testing the waters with a short answer.

+>+>++>++>++>++++>++[>[<+++++>-]<<]>
>++<
[
    >[->>+>+<<<]
    >>>
    [
        <[-<+<+>>]
        <[->+<]
        >>-
    ]
    <[-]<<<-
]
>.

The ↑↑ indicate Knuth's arrow notation, where a single ↑, such as X↑Y, means (((X*Y)*Y)*Y)... X times = X^Y, and two ↑↑s means (((X↑Y)↑Y)↑Y)... X times. For example, 2↑↑4 = 2²²².

(I'm not familiar with bignum notation, so please tell me if there's a shorter way of representing this, or there's an error in my calculations)

Explanation:

+>+>++>++>++>++++>++[>[<+++++>-]<<]>

Produces the number 45306. (Taken from the brainfuck constants page on Esolangs, an immensely useful page). This will be used as the counter.

>++< 

Sets the current value as two and move back to the counter

[ Loop until the counter is 0

    Square the current value
    >[->>+>+<<<]
    >>>
    [
        <[-<+<+>>]
        <[->+<]
        >>-
    ]<[-]

    Decrement the counter
    <<<-
]

A few ways to extend this:

• Increase the counter. Pretty easy to do.
• Increase the initial value. To be simple, you could just set the initial value and the counter as the same number
• Remove the clear cell in the squaring operation, which compounds the result
• Create another counter and put another loop around the whole thing
  • This effectively adds another Knuth's Arrow to the result (I think)
  • Further addition, for each iteration of the outer loop, copy the current value to use as the inner loop's counter
  • And then put another loop around the whole lot again.