Coding a Bitcoin mining program in C is an interesting project, but it's quite complex and requires a deep understanding of both the Bitcoin protocol and low-level programming. Here's a high-level overview of what you'd need to do:

1. Implement SHA-256 hashing algorithm
2. Connect to the Bitcoin network
3. Retrieve the current block header and transaction data
4. Construct a valid block header
5. Perform the mining operation (repeatedly hash the block header while incrementing the nonce)
6. Submit a solution if found

For learning purposes, you might want to start with a simplified version that just focuses on the core hashing part. Here's a very basic example to get you started:

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#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <openssl/sha.h>

#define BLOCK_HEADER_SIZE 80

void sha256(unsigned char *data, size_t len, unsigned char*hash) {
    SHA256_CTX sha256;
    SHA256_Init(&sha256);
    SHA256_Update(&sha256, data, len);
    SHA256_Final(hash, &sha256);
}

int main() {
    unsigned char block_header[BLOCK_HEADER_SIZE] = {0};
    unsigned char hash[SHA256_DIGEST_LENGTH];
    unsigned int nonce = 0;

    // In a real scenario, you'd fill the block_header with actual data
    // For this example, we'll just increment the nonce

    while (1) {
        // Update nonce in block header
        memcpy(block_header + 76, &nonce, 4);

        // Perform double SHA-256 hash
        sha256(block_header, BLOCK_HEADER_SIZE, hash);
        sha256(hash, SHA256_DIGEST_LENGTH, hash);

        // Check if hash meets difficulty requirement (simplified)
        if (hash[0] == 0 && hash[1] == 0) {
            printf("Solution found! Nonce: %u\n", nonce);
            break;
        }

        nonce++;
    }

    return 0;
}

To compile this, you'll need to link against the OpenSSL library:

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gcc -o bitcoin_miner bitcoin_miner.c -lcrypto

This is a very simplified version and doesn't actually connect to the Bitcoin network or validate real blocks. It just demonstrates the core concept of repeatedly hashing data while incrementing a nonce until a hash with a certain property is found.

For a full Bitcoin mining implementation, you'd need to dive much deeper into the Bitcoin protocol, network communication, and optimize heavily for performance. Also, keep in mind that CPU mining for Bitcoin is extremely inefficient compared to specialized ASIC hardware.

If you're interested in learning more about cryptocurrency mining, you might want to look into mining alt-coins that are still ASIC-resistant, or consider contributing to an open-source mining project to learn from existing codebases.