Home/Chain Registry/Block #2,646,057

Block #2,646,057

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 5/3/2018, 4:35:48 AM · Difficulty 11.7440 · 4,192,813 confirmations

1CC

Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header

Block Hash

099f2d70dd9fb74f88369cae7ae0f74b4db5ee6cd0acc9f84d040b3eef1fdc53

View on Chainz ↗

Height

#2,646,057

Difficulty

11.743973

Transactions

Size

609 B

Version

Bits

0bbe7508

Nonce

451,388,837

Timestamp

5/3/2018, 4:35:48 AM

Confirmations

4,192,813

Merkle Root

67179670fc82c8148409c952f6579497063b433a5ff62136d586742e27d42981

Transactions (2)

Coinbasee4c813572f647a…a9c0e7ab799719

1 in → 1 out7.2500 XPM110 B

AcZbZozc…QLTPmmGM

8f097cf906031f…d954fd1eb1e773

2 in → 3 out37.1950 XPM408 B

AP7MSvKo…HezATyf5 AHmoHaoV…guxDRZ3w ARznVePF…S7wvbB9s

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.835 × 10⁹⁷(98-digit number)

28351188285319045443…77292099577454561280

Discovered Prime Numbers

p_k = 2^k × origin − 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

origin − 1

2.835 × 10⁹⁷(98-digit number)

28351188285319045443…77292099577454561279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.670 × 10⁹⁷(98-digit number)

56702376570638090886…54584199154909122559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.134 × 10⁹⁸(99-digit number)

11340475314127618177…09168398309818245119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.268 × 10⁹⁸(99-digit number)

22680950628255236354…18336796619636490239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.536 × 10⁹⁸(99-digit number)

45361901256510472708…36673593239272980479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.072 × 10⁹⁸(99-digit number)

90723802513020945417…73347186478545960959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.814 × 10⁹⁹(100-digit number)

18144760502604189083…46694372957091921919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.628 × 10⁹⁹(100-digit number)

36289521005208378167…93388745914183843839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.257 × 10⁹⁹(100-digit number)

72579042010416756334…86777491828367687679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.451 × 10¹⁰⁰(101-digit number)

14515808402083351266…73554983656735375359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

2.903 × 10¹⁰⁰(101-digit number)

29031616804166702533…47109967313470750719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page →

★★★☆☆

Rarity

RareChain length 11

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 2646057

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock 099f2d70dd9fb74f88369cae7ae0f74b4db5ee6cd0acc9f84d040b3eef1fdc53

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #2,646,057 on Chainz ↗

Block #2,646,057

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