Home/Chain Registry/Block #373,277

Block #373,277

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/24/2014, 5:01:48 AM · Difficulty 10.4251 · 6,452,853 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

d767e2c936c14ad9849944b5d78570059835c10ff87f0be9a88185fa57a912fe

View on Chainz ↗

Height

#373,277

Difficulty

10.425085

Transactions

Size

814 B

Version

Bits

0a6cd260

Nonce

67,112,458

Timestamp

1/24/2014, 5:01:48 AM

Confirmations

6,452,853

Merkle Root

4548f128a271354790e7b72c04f8b66ebb27874d2a2342b5e0b895254eaa204b

Transactions (4)

Coinbase44ae7f119af530…14ad26e5bf2fe6

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

55591203a5f94d…c0e09744ffde12

1 in → 1 out9.1700 XPM158 B

Ab1g4SX5…KtCxyybc

e449082cd5e376…f68226712a0889

1 in → 2 out4.9939 XPM225 B

AGT2XXiE…QadPN7Zm AKSPTxA6…EhpdVvKD

230349d8aa1fbf…bea84ff1e42c4e

1 in → 2 out4.0488 XPM225 B

AVYuRWRg…1NnfMdT3 AJz987nj…X2bMmzq6

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.

6.260 × 10⁹⁴(95-digit number)

62608164244847738672…75889780596211091600

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

6.260 × 10⁹⁴(95-digit number)

62608164244847738672…75889780596211091601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.252 × 10⁹⁵(96-digit number)

12521632848969547734…51779561192422183201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.504 × 10⁹⁵(96-digit number)

25043265697939095469…03559122384844366401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

5.008 × 10⁹⁵(96-digit number)

50086531395878190938…07118244769688732801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.001 × 10⁹⁶(97-digit number)

10017306279175638187…14236489539377465601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.003 × 10⁹⁶(97-digit number)

20034612558351276375…28472979078754931201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.006 × 10⁹⁶(97-digit number)

40069225116702552750…56945958157509862401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

8.013 × 10⁹⁶(97-digit number)

80138450233405105501…13891916315019724801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.602 × 10⁹⁷(98-digit number)

16027690046681021100…27783832630039449601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.205 × 10⁹⁷(98-digit number)

32055380093362042200…55567665260078899201

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second 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

UncommonChain length 10

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 2CC formula:

2CC: 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 373277

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 d767e2c936c14ad9849944b5d78570059835c10ff87f0be9a88185fa57a912fe

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 #373,277 on Chainz ↗

Block #373,277

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