Home/Chain Registry/Block #329,978

Block #329,978

2CCLength 12★★★★☆

Cunningham Chain of the Second Kind · Discovered 12/26/2013, 8:47:15 AM · Difficulty 10.1677 · 6,484,098 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

310dfa040f8eeb9b64372445bff93024eadd402b8cd013eea81a053075f23edd

View on Chainz ↗

Height

#329,978

Difficulty

10.167659

Transactions

Size

208 B

Version

Bits

0a2aebbb

Nonce

26,976

Timestamp

12/26/2013, 8:47:15 AM

Confirmations

6,484,098

Merkle Root

1ae6d37620ec0fc0e64672767c478007244a7c20d5747de8501c8d35bafa552b

Transactions (1)

Coinbase1ae6d37620ec0f…1c8d35bafa552b

1 in → 1 out9.6600 XPM116 B

AbwWkWZt…kawDhufa

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.

7.936 × 10⁹⁹(100-digit number)

79366573531178191852…31757963887352371200

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

7.936 × 10⁹⁹(100-digit number)

79366573531178191852…31757963887352371201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.587 × 10¹⁰⁰(101-digit number)

15873314706235638370…63515927774704742401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.174 × 10¹⁰⁰(101-digit number)

31746629412471276741…27031855549409484801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.349 × 10¹⁰⁰(101-digit number)

63493258824942553482…54063711098818969601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.269 × 10¹⁰¹(102-digit number)

12698651764988510696…08127422197637939201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.539 × 10¹⁰¹(102-digit number)

25397303529977021392…16254844395275878401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.079 × 10¹⁰¹(102-digit number)

50794607059954042785…32509688790551756801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.015 × 10¹⁰²(103-digit number)

10158921411990808557…65019377581103513601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.031 × 10¹⁰²(103-digit number)

20317842823981617114…30038755162207027201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.063 × 10¹⁰²(103-digit number)

40635685647963234228…60077510324414054401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

8.127 × 10¹⁰²(103-digit number)

81271371295926468456…20155020648828108801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^11 × origin + 1

1.625 × 10¹⁰³(104-digit number)

16254274259185293691…40310041297656217601

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

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 329978

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 310dfa040f8eeb9b64372445bff93024eadd402b8cd013eea81a053075f23edd

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 #329,978 on Chainz ↗

Block #329,978

Cookie Preferences