Block #75,201

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/21/2013, 3:12:44 PM · Difficulty 8.9960 · 6,721,590 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

3216004c4e436c118ac300e7228a5a2258bb2240b31473796cc42b07e3a30af4

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Height

#75,201

Difficulty

8.995968

Transactions

Size

202 B

Version

Bits

08fef7be

Nonce

Timestamp

7/21/2013, 3:12:44 PM

Confirmations

6,721,590

Mined by

⛏️ P2SHAZDgU5ryLDBgQ43WTK1SQdESypdmcwdqVC

Merkle Root

6cc5156c59981abfc072814c524e044beb30fafd6707247cbe38748d6019b08d

Transactions (1)

Coinbase6cc5156c59981a…38748d6019b08d

1 in → 1 out12.3400 XPM110 B

AZDgU5ry…dmcwdqVC

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.

3.389 × 10⁹⁹(100-digit number)

33895714130086432800…70013052658777903121

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

3.389 × 10⁹⁹(100-digit number)

33895714130086432800…70013052658777903121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.779 × 10⁹⁹(100-digit number)

67791428260172865601…40026105317555806241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.355 × 10¹⁰⁰(101-digit number)

13558285652034573120…80052210635111612481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.711 × 10¹⁰⁰(101-digit number)

27116571304069146240…60104421270223224961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.423 × 10¹⁰⁰(101-digit number)

54233142608138292480…20208842540446449921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.084 × 10¹⁰¹(102-digit number)

10846628521627658496…40417685080892899841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.169 × 10¹⁰¹(102-digit number)

21693257043255316992…80835370161785799681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.338 × 10¹⁰¹(102-digit number)

43386514086510633984…61670740323571599361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.677 × 10¹⁰¹(102-digit number)

86773028173021267969…23341480647143198721

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