Block #204,228

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/11/2013, 8:55:14 AM · Difficulty 9.8983 · 6,585,670 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

09478538f7e8d763cb19009b62825b325a1f593a5fea4c674cb7a19f3e0068bb

View on Chainz ↗

Height

#204,228

Difficulty

9.898334

Transactions

Size

796 B

Version

Bits

09e5f93a

Nonce

243,318

Timestamp

10/11/2013, 8:55:14 AM

Confirmations

6,585,670

Merkle Root

6747153a4c944b31329905041ea7b8cfb4568557afb3e92e394203a93f5fbacf

Transactions (3)

Coinbase6e724709a7b156…216284a8cbd68c

1 in → 1 out10.2100 XPM109 B

AKyKBBF5…Q9vxBLNg

af810e50e8a168…d152f82f56f5a7

2 in → 2 out18.3871 XPM374 B

AGfpuAXN…67crvESZ ASuoUi24…FwBoFbxd

4ac6fb2b09888c…d11e7077dd4495

1 in → 2 out8.1850 XPM225 B

AJc9qbGx…weCAN8zR AMqy1Z9q…9qLErWJg

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.

9.990 × 10⁸⁸(89-digit number)

99907123617366722519…66333405729525806001

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

9.990 × 10⁸⁸(89-digit number)

99907123617366722519…66333405729525806001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.998 × 10⁸⁹(90-digit number)

19981424723473344503…32666811459051612001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.996 × 10⁸⁹(90-digit number)

39962849446946689007…65333622918103224001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.992 × 10⁸⁹(90-digit number)

79925698893893378015…30667245836206448001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.598 × 10⁹⁰(91-digit number)

15985139778778675603…61334491672412896001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.197 × 10⁹⁰(91-digit number)

31970279557557351206…22668983344825792001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.394 × 10⁹⁰(91-digit number)

63940559115114702412…45337966689651584001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.278 × 10⁹¹(92-digit number)

12788111823022940482…90675933379303168001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.557 × 10⁹¹(92-digit number)

25576223646045880965…81351866758606336001

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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, …

Cross-reference on Chainz Explorer