Home/Chain Registry/Block #359,244

Block #359,244

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/14/2014, 4:06:09 PM · Difficulty 10.3881 · 6,467,562 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

a682660c2d1c00f03ef30ac7cc6375bcf2ae9f80498ea08e82627aff44292cfe

View on Chainz ↗

Height

#359,244

Difficulty

10.388109

Transactions

Size

1.88 KB

Version

Bits

0a635b16

Nonce

152,619

Timestamp

1/14/2014, 4:06:09 PM

Confirmations

6,467,562

Merkle Root

f74b36908c3edb6f88cf8d6cd164a6714390512eab489e53f4af15827038785b

Transactions (4)

Coinbase82f94f64ffb089…e10968b307d9e1

1 in → 26 out9.2500 XPM947 B

AQvZBsUo…hppgRZTJ AZV4TwxQ…8JnQqSoH Aac9Hjdg…P4ktypc3 AMbCuLHZ…WSoStwkc Ac7TsAMG…2W5MRTA8

c3ff328fe60fcb…2510bf948c576a

1 in → 2 out9.2800 XPM225 B

ALGZehKy…ys7zPqFp AWL1MkCE…xUvJQzKi

d8af15b957ec40…aab15700d77168

2 in → 6 out18.8200 XPM441 B

AMMSpxFF…5AwmfBJ2 AXDEZh15…FbrAPGkC AK3vz3dH…9NvorskL AeKNrjNj…1NEq95Ta AMmkoL9c…RfSSCaRk

4e63b5ead89997…0aa7889060673a

1 in → 2 out9.2800 XPM225 B

AS7rq4SW…Dzuc8thg Ad7pk5XR…Y9bNgHhy

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.

7.972 × 10⁹²(93-digit number)

79723564241156925261…44697879745862512640

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

7.972 × 10⁹²(93-digit number)

79723564241156925261…44697879745862512641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.594 × 10⁹³(94-digit number)

15944712848231385052…89395759491725025281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.188 × 10⁹³(94-digit number)

31889425696462770104…78791518983450050561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.377 × 10⁹³(94-digit number)

63778851392925540208…57583037966900101121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.275 × 10⁹⁴(95-digit number)

12755770278585108041…15166075933800202241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.551 × 10⁹⁴(95-digit number)

25511540557170216083…30332151867600404481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.102 × 10⁹⁴(95-digit number)

51023081114340432167…60664303735200808961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.020 × 10⁹⁵(96-digit number)

10204616222868086433…21328607470401617921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.040 × 10⁹⁵(96-digit number)

20409232445736172866…42657214940803235841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.081 × 10⁹⁵(96-digit number)

40818464891472345733…85314429881606471681

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 359244

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 a682660c2d1c00f03ef30ac7cc6375bcf2ae9f80498ea08e82627aff44292cfe

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 #359,244 on Chainz ↗

Block #359,244

Cookie Preferences