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Success with nonce 84561291 Hash is 0000001f0ea21e676b6dde5ad429b9d131a9f2b000802ab2f169cbca22b1e21a Elapsed Time: 665.0949 seconds Hashing Power: 127141 hashes per second As you can see, increasing the difficulty by 1 bit causes an exponential increase in the time it takes to find a solution. If you think of the entire 256-bit number space, each time you constrain one more bit to zero, you decrease the search space by half. In the example above, it takes 84 million hash attempts to find a nonce that produces a hash with 26 leading bits as zero. Even at a speed of more than 120 thousand hashes per second, it still requires ten minutes on a consumer laptop to find this solution. At the time of writing this, the network is attempting to find a block whose header hash is less than 000000000000004c296e6376db3a241271f43fd3f5de7ba18986e517a243baa7. As you can see, there are a lot of zeroes at the beginning of that hash, meaning that the acceptable range of hashes is much smaller, hence more difficult to find a valid hash. It will take on average more than 150 quadrillion hash calculations per second for the network to discover the next block. That seems like an impossible task, but fortunately the network is bringing 100 Peta Hashes per second of processing power to bear, which will be able to find a block in about 10 minutes on average. Difficulty Representation In Example 8-3 we saw that the block contains the difficulty target, in a notation called “difficulty bits” or just “bits”, which in block 277,316 has the value of 0x1903a30c. This notation expresses the difficulty target as a coefficient/exponent format, with the first two hexadecimal digits for the exponent and the next six hex digits as the coefficient. In this block, therefore, the exponent is 0x19 and the coefficient is 0x03a30c. The formula to calculate the difficulty target from this representation is: target = coefficient * 2^(8 * (exponent - 3)) Using that formula, and the difficulty bits value 0x1903a30c, we get: target = 0x03a30c * 2(0x08 * (0x19 - 0x03)) ⇒ target = 0x03a30c * 2(0x08 * 0x16) ⇒ target = 0x03a30c * 20xB0 which in decimal is: ⇒ target = 238,348 * 2176 ⇒ target = 22,829,202,948,393,929,850,749,706,076,701,368,331,072,452,018,388,575,715,328 198 | Chapter 8: Mining and ConsensusPDF Image | Mastering Bitcoin
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