Has anyone tried this approach? The count of powers of 2 as sum?
Number 1: 2^0
Number 3: 2^0 + 2^1
Number 7: 2^0 + 2^1 + 2^2
Number 8: 2^3
Number 21: 2^0 + 2^2 + 2^4
Number 49: 2^0 + 2^4 + 2^5
Number 76: 2^2 + 2^3 + 2^6
Number 224: 2^5 + 2^6 + 2^7
Number 467: 2^0 + 2^1 + 2^4 + 2^6 + 2^7 + 2^8
Number 514: 2^1 + 2^9
Number 1155: 2^0 + 2^1 + 2^7 + 2^10
Number 2683: 2^0 + 2^1 + 2^3 + 2^4 + 2^5 + 2^6 + 2^9 + 2^11
Number 5216: 2^5 + 2^6 + 2^10 + 2^12
Number 10544: 2^4 + 2^5 + 2^8 + 2^11 + 2^13
Number 26867: 2^0 + 2^1 + 2^4 + 2^5 + 2^6 + 2^7 + 2^11 + 2^13 + 2^14
Number 51510: 2^1 + 2^2 + 2^4 + 2^5 + 2^8 + 2^11 + 2^14 + 2^15
Number 95823: 2^0 + 2^1 + 2^2 + 2^3 + 2^6 + 2^9 + 2^10 + 2^12 + 2^13 + 2^14 + 2^16
Number 198669: 2^0 + 2^2 + 2^3 + 2^11 + 2^16 + 2^17
Number 357535: 2^0 + 2^1 + 2^2 + 2^3 + 2^4 + 2^7 + 2^10 + 2^12 + 2^13 + 2^14 + 2^16 + 2^18
Number 863317: 2^0 + 2^2 + 2^4 + 2^6 + 2^10 + 2^11 + 2^13 + 2^16 + 2^18 + 2^19
Number 1811764: 2^2 + 2^4 + 2^5 + 2^8 + 2^10 + 2^13 + 2^15 + 2^16 + 2^17 + 2^19 + 2^20
Number 3007503: 2^0 + 2^1 + 2^2 + 2^3 + 2^10 + 2^13 + 2^14 + 2^15 + 2^16 + 2^18 + 2^19 + 2^21
Number 5598802: 2^1 + 2^4 + 2^6 + 2^9 + 2^10 + 2^11 + 2^13 + 2^14 + 2^16 + 2^18 + 2^20 + 2^22
Number 14428676: 2^2 + 2^9 + 2^11 + 2^13 + 2^18 + 2^19 + 2^20 + 2^22 + 2^23
Number 33185509: 2^0 + 2^2 + 2^5 + 2^6 + 2^7 + 2^9 + 2^10 + 2^11 + 2^12 + 2^14 + 2^17 + 2^19 + 2^20 + 2^21 + 2^22 + 2^23 + 2^24
Number 54538862: 2^1 + 2^2 + 2^3 + 2^5 + 2^6 + 2^9 + 2^12 + 2^13 + 2^22 + 2^24 + 2^25
Number 111949941: 2^0 + 2^2 + 2^4 + 2^5 + 2^6 + 2^11 + 2^12 + 2^13 + 2^18 + 2^19 + 2^21 + 2^23 + 2^25 + 2^26
Number 227634408: 2^3 + 2^5 + 2^6 + 2^7 + 2^10 + 2^11 + 2^13 + 2^14 + 2^16 + 2^20 + 2^23 + 2^24 + 2^26 + 2^27
Number 400708894: 2^1 + 2^2 + 2^3 + 2^4 + 2^8 + 2^10 + 2^12 + 2^14 + 2^17 + 2^21 + 2^22 + 2^23 + 2^24 + 2^25 + 2^26 + 2^28
Number 1033162084: 2^2 + 2^5 + 2^6 + 2^8 + 2^10 + 2^11 + 2^14 + 2^15 + 2^18 + 2^20 + 2^23 + 2^24 + 2^26 + 2^27 + 2^28 + 2^29
Number 2102388551: 2^0 + 2^1 + 2^2 + 2^6 + 2^8 + 2^9 + 2^10 + 2^13 + 2^14 + 2^15 + 2^16 + 2^17 + 2^18 + 2^19 + 2^22 + 2^24 + 2^26 + 2^27 + 2^28 + 2^29 + 2^30
Number 3093472814: 2^1 + 2^2 + 2^3 + 2^5 + 2^9 + 2^10 + 2^13 + 2^15 + 2^17 + 2^21 + 2^22 + 2^27 + 2^28 + 2^29 + 2^31
Number 7137437912: 2^3 + 2^4 + 2^6 + 2^7 + 2^11 + 2^13 + 2^15 + 2^18 + 2^19 + 2^21 + 2^22 + 2^24 + 2^27 + 2^29 + 2^31 + 2^32
Number 14133072157: 2^0 + 2^2 + 2^3 + 2^4 + 2^8 + 2^12 + 2^15 + 2^16 + 2^18 + 2^21 + 2^22 + 2^25 + 2^27 + 2^30 + 2^32 + 2^33
Number 20112871792: 2^4 + 2^5 + 2^6 + 2^8 + 2^12 + 2^17 + 2^20 + 2^22 + 2^23 + 2^25 + 2^26 + 2^27 + 2^29 + 2^31 + 2^34
Number 42387769980: 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^9 + 2^11 + 2^17 + 2^23 + 2^25 + 2^26 + 2^27 + 2^28 + 2^30 + 2^31 + 2^32 + 2^35
Number 100251560595: 2^0 + 2^1 + 2^4 + 2^7 + 2^9 + 2^11 + 2^13 + 2^14 + 2^16 + 2^18 + 2^20 + 2^21 + 2^22 + 2^24 + 2^25 + 2^26 + 2^28 + 2^30 + 2^32 + 2^33 + 2^34 + 2^36
Number 146971536592: 2^4 + 2^6 + 2^7 + 2^10 + 2^11 + 2^13 + 2^15 + 2^16 + 2^17 + 2^18 + 2^19 + 2^21 + 2^27 + 2^28 + 2^29 + 2^33 + 2^37
Number 323724968937: 2^0 + 2^3 + 2^5 + 2^6 + 2^7 + 2^8 + 2^9 + 2^16 + 2^17 + 2^23 + 2^24 + 2^25 + 2^26 + 2^27 + 2^28 + 2^30 + 2^32 + 2^33 + 2^35 + 2^38
Number 1003651412950: 2^1 + 2^2 + 2^4 + 2^6 + 2^7 + 2^8 + 2^9 + 2^12 + 2^13 + 2^16 + 2^19 + 2^22 + 2^25 + 2^26 + 2^27 + 2^29 + 2^31 + 2^32 + 2^35 + 2^37 + 2^38 + 2^39
Number 1458252205147: 2^0 + 2^1 + 2^3 + 2^4 + 2^6 + 2^10 + 2^11 + 2^14 + 2^15 + 2^17 + 2^19 + 2^20 + 2^23 + 2^25 + 2^26 + 2^31 + 2^32 + 2^33 + 2^36 + 2^38 + 2^40
Number 2895374552463: 2^0 + 2^1 + 2^2 + 2^3 + 2^7 + 2^8 + 2^10 + 2^11 + 2^15 + 2^16 + 2^18 + 2^22 + 2^23 + 2^24 + 2^29 + 2^33 + 2^37 + 2^39 + 2^41
Number 7409811047825: 2^0 + 2^4 + 2^7 + 2^8 + 2^10 + 2^14 + 2^15 + 2^16 + 2^17 + 2^18 + 2^21 + 2^24 + 2^25 + 2^27 + 2^28 + 2^29 + 2^32 + 2^34 + 2^35 + 2^36 + 2^37 + 2^39 + 2^41 + 2^42
Number 15404761757071: 2^0 + 2^1 + 2^2 + 2^3 + 2^7 + 2^8 + 2^10 + 2^12 + 2^13 + 2^17 + 2^19 + 2^20 + 2^22 + 2^24 + 2^25 + 2^28 + 2^29 + 2^31 + 2^33 + 2^41 + 2^42 + 2^43
Number 19996463086597: 2^0 + 2^2 + 2^10 + 2^11 + 2^12 + 2^13 + 2^18 + 2^20 + 2^25 + 2^27 + 2^30 + 2^31 + 2^32 + 2^33 + 2^34 + 2^35 + 2^37 + 2^41 + 2^44
Number 51408670348612: 2^2 + 2^6 + 2^8 + 2^10 + 2^12 + 2^14 + 2^15 + 2^19 + 2^23 + 2^24 + 2^25 + 2^31 + 2^32 + 2^38 + 2^39 + 2^41 + 2^42 + 2^43 + 2^45
Number 119666659114170: 2^1 + 2^3 + 2^4 + 2^5 + 2^7 + 2^10 + 2^11 + 2^12 + 2^13 + 2^16 + 2^18 + 2^20 + 2^21 + 2^23 + 2^28 + 2^33 + 2^34 + 2^36 + 2^38 + 2^39 + 2^42 + 2^43 + 2^45 + 2^46
Number 191206974700443: 2^0 + 2^1 + 2^3 + 2^4 + 2^7 + 2^8 + 2^9 + 2^11 + 2^12 + 2^13 + 2^17 + 2^18 + 2^19 + 2^22 + 2^23 + 2^24 + 2^25 + 2^26 + 2^28 + 2^30 + 2^31 + 2^33 + 2^34 + 2^37 + 2^38 + 2^39 + 2^40 + 2^42 + 2^43 + 2^45 + 2^47
Number 409118905032525: 2^0 + 2^2 + 2^3 + 2^6 + 2^8 + 2^9 + 2^10 + 2^11 + 2^12 + 2^14 + 2^16 + 2^24 + 2^25 + 2^27 + 2^29 + 2^30 + 2^32 + 2^33 + 2^34 + 2^36 + 2^42 + 2^44 + 2^45 + 2^46 + 2^48
Number 611140496167764: 2^2 + 2^4 + 2^6 + 2^8 + 2^9 + 2^12 + 2^15 + 2^17 + 2^18 + 2^19 + 2^21 + 2^26 + 2^27 + 2^28 + 2^29 + 2^34 + 2^36 + 2^38 + 2^39 + 2^40 + 2^41 + 2^43 + 2^45 + 2^49
Number 2058769515153876: 2^2 + 2^4 + 2^6 + 2^7 + 2^8 + 2^11 + 2^21 + 2^23 + 2^24 + 2^29 + 2^31 + 2^36 + 2^37 + 2^38 + 2^44 + 2^46 + 2^48 + 2^49 + 2^50
Number 4216495639600700: 2^2 + 2^3 + 2^4 + 2^5 + 2^9 + 2^10 + 2^11 + 2^12 + 2^15 + 2^16 + 2^17 + 2^19 + 2^22 + 2^23 + 2^26 + 2^29 + 2^30 + 2^32 + 2^37 + 2^38 + 2^39 + 2^41 + 2^43 + 2^44 + 2^45 + 2^46 + 2^47 + 2^49 + 2^50 + 2^51
Number 6763683971478124: 2^2 + 2^3 + 2^5 + 2^6 + 2^9 + 2^12 + 2^13 + 2^17 + 2^18 + 2^19 + 2^20 + 2^21 + 2^22 + 2^26 + 2^29 + 2^30 + 2^31 + 2^35 + 2^39 + 2^40 + 2^41 + 2^42 + 2^51 + 2^52
Number 9974455244496707: 2^0 + 2^1 + 2^6 + 2^8 + 2^9 + 2^10 + 2^11 + 2^12 + 2^16 + 2^18 + 2^19 + 2^21 + 2^23 + 2^24 + 2^26 + 2^28 + 2^30 + 2^31 + 2^33 + 2^34 + 2^36 + 2^37 + 2^39 + 2^40 + 2^41 + 2^42 + 2^43 + 2^45 + 2^46 + 2^48 + 2^49 + 2^53
Number 30045390491869460: 2^2 + 2^4 + 2^8 + 2^13 + 2^14 + 2^15 + 2^16 + 2^17 + 2^18 + 2^21 + 2^22 + 2^24 + 2^25 + 2^27 + 2^28 + 2^31 + 2^32 + 2^33 + 2^34 + 2^35 + 2^36 + 2^41 + 2^42 + 2^43 + 2^44 + 2^45 + 2^47 + 2^49 + 2^51 + 2^53 + 2^54
Number 44218742292676575: 2^0 + 2^1 + 2^2 + 2^3 + 2^4 + 2^6 + 2^7 + 2^8 + 2^9 + 2^10 + 2^11 + 2^12 + 2^13 + 2^14 + 2^15 + 2^18 + 2^22 + 2^23 + 2^25 + 2^27 + 2^28 + 2^29 + 2^33 + 2^34 + 2^36 + 2^37 + 2^39 + 2^43 + 2^44 + 2^48 + 2^50 + 2^51 + 2^52 + 2^55
Number 138245758910846492: 2^2 + 2^3 + 2^4 + 2^9 + 2^10 + 2^12 + 2^14 + 2^15 + 2^16 + 2^18 + 2^20 + 2^23 + 2^24 + 2^25 + 2^26 + 2^32 + 2^35 + 2^38 + 2^39 + 2^40 + 2^42 + 2^45 + 2^48 + 2^49 + 2^51 + 2^53 + 2^54 + 2^55 + 2^56
Number 199976667976342049: 2^0 + 2^5 + 2^9 + 2^11 + 2^12 + 2^15 + 2^19 + 2^20 + 2^25 + 2^28 + 2^30 + 2^35 + 2^36 + 2^37 + 2^39 + 2^40 + 2^42 + 2^44 + 2^45 + 2^46 + 2^49 + 2^50 + 2^54 + 2^55 + 2^57
Number 525070384258266191: 2^0 + 2^1 + 2^2 + 2^3 + 2^6 + 2^10 + 2^12 + 2^13 + 2^15 + 2^17 + 2^19 + 2^22 + 2^23 + 2^24 + 2^25 + 2^26 + 2^31 + 2^32 + 2^33 + 2^35 + 2^36 + 2^37 + 2^39 + 2^42 + 2^43 + 2^45 + 2^46 + 2^48 + 2^51 + 2^54 + 2^56 + 2^57 + 2^58
Number 1135041350219496382: 2^1 + 2^2 + 2^3 + 2^4 + 2^5 + 2^7 + 2^8 + 2^9 + 2^11 + 2^12 + 2^13 + 2^14 + 2^17 + 2^18 + 2^20 + 2^21 + 2^24 + 2^26 + 2^29 + 2^35 + 2^36 + 2^41 + 2^43 + 2^44 + 2^45 + 2^46 + 2^54 + 2^55 + 2^56 + 2^57 + 2^58 + 2^59
Number 1425787542618654982: 2^1 + 2^2 + 2^8 + 2^11 + 2^14 + 2^17 + 2^18 + 2^20 + 2^21 + 2^22 + 2^23 + 2^25 + 2^30 + 2^32 + 2^33 + 2^34 + 2^36 + 2^37 + 2^41 + 2^43 + 2^45 + 2^46 + 2^48 + 2^51 + 2^54 + 2^55 + 2^56 + 2^57 + 2^60
Number 3908372542507822062: 2^1 + 2^2 + 2^3 + 2^5 + 2^6 + 2^7 + 2^8 + 2^9 + 2^11 + 2^13 + 2^15 + 2^16 + 2^20 + 2^25 + 2^26 + 2^28 + 2^29 + 2^31 + 2^33 + 2^34 + 2^35 + 2^36 + 2^42 + 2^44 + 2^46 + 2^48 + 2^50 + 2^51 + 2^52 + 2^53 + 2^57 + 2^58 + 2^60 + 2^61
Number 8993229949524469768: 2^3 + 2^11 + 2^13 + 2^14 + 2^16 + 2^17 + 2^18 + 2^19 + 2^22 + 2^23 + 2^26 + 2^27 + 2^29 + 2^31 + 2^32 + 2^34 + 2^35 + 2^36 + 2^37 + 2^38 + 2^39 + 2^41 + 2^42 + 2^43 + 2^44 + 2^46 + 2^49 + 2^50 + 2^51 + 2^54 + 2^55 + 2^58 + 2^59 + 2^60 + 2^61 + 2^62
Number 17799667357578236628: 2^2 + 2^4 + 2^6 + 2^7 + 2^9 + 2^12 + 2^16 + 2^20 + 2^23 + 2^28 + 2^29 + 2^31 + 2^32 + 2^33 + 2^34 + 2^37 + 2^40 + 2^41 + 2^42 + 2^43 + 2^44 + 2^48 + 2^50 + 2^56 + 2^57 + 2^58 + 2^60 + 2^61 + 2^62 + 2^63
Number 30568377312064202855: 2^0 + 2^1 + 2^2 + 2^5 + 2^6 + 2^11 + 2^13 + 2^14 + 2^17 + 2^20 + 2^21 + 2^23 + 2^24 + 2^26 + 2^32 + 2^34 + 2^36 + 2^37 + 2^40 + 2^44 + 2^45 + 2^47 + 2^51 + 2^52 + 2^53 + 2^59 + 2^61 + 2^63 + 2^64
I wrote a small script to try this but if someone can make multy gpu Windows/Linux program with that approach to try it
import bitcoin
import ecdsa
import base58
import random
import logging
# Function to convert private key to Wallet Import Format (WIF)
def private_key_to_wif(private_key):
wif = bitcoin.encode_privkey(bitcoin.decode_privkey(private_key, 'hex'), 'wif')
return wif
# Function to convert private key to Bitcoin address (P2PKH)
def private_key_to_address(private_key):
sk = ecdsa.SigningKey.from_string(bytes.fromhex(private_key), curve=ecdsa.SECP256k1)
vk = sk.get_verifying_key()
compressed_vk = vk.to_string('compressed').hex()
address = bitcoin.pubkey_to_address(compressed_vk)
return address
# Function to calculate Hash 160 of a Bitcoin address
def address_to_hash160(address):
decoded_address = base58.b58decode_check(address)
return decoded_address[1:].hex()
# Function to generate a Bitcoin private key and check if the corresponding address matches the target address
def generate_private_key(target_hash160):
while True:
try:
num_objects = random.randint(27,35)
random_values = random.sample(range(0, 65), num_objects)
random_values.append(65)
private_key_num = sum([2 ** power for power in random_values])
private_key = format(private_key_num, '064x')
bitcoin_address = private_key_to_address(private_key)
hash160 = address_to_hash160(bitcoin_address)
print("Private Key:", private_key)
if hash160 == target_hash160:
with open('private_key.txt', 'w') as file:
file.write(private_key)
logging.info("Private key saved to 'private_key.txt' file.")
break
except Exception as e:
logging.error(f"Error: {str(e)}")
def main():
target_hash160 = '20d45a6a762535700ce9e0b216e31994335db8a5'
logging.basicConfig(filename='bitcoin_keygen.log', level=logging.INFO, format='%(asctime)s - %(levelname)s - %(message)s')
logging.info("Generating private keys...")
generate_private_key(target_hash160)
if __name__ == "__main__":
main()