Block #75,406

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/21/2013, 4:18:45 PM · Difficulty 8.9961 · 6,720,642 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

1de7a2d3fdb4eb43aed38e48647f12d4732eaf54c8f24c73c76855c9ba69316e

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Height

#75,406

Difficulty

8.996085

Transactions

Size

202 B

Version

Bits

08feff67

Nonce

1,484

Timestamp

7/21/2013, 4:18:45 PM

Confirmations

6,720,642

Mined by

⛏️ P2SHAeVvGUh4cnFPF4FMDsxtGiaqQhkYpQ2wDQ

Merkle Root

6e5840616c3741d7722738d8b2168d51704d185282434cc445db1365bea40222

Transactions (1)

Coinbase6e5840616c3741…db1365bea40222

1 in → 1 out12.3400 XPM109 B

AeVvGUh4…kYpQ2wDQ

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.

5.385 × 10¹⁰⁰(101-digit number)

53859548360249070144…18647575202846147901

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

5.385 × 10¹⁰⁰(101-digit number)

53859548360249070144…18647575202846147901

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.077 × 10¹⁰¹(102-digit number)

10771909672049814028…37295150405692295801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.154 × 10¹⁰¹(102-digit number)

21543819344099628057…74590300811384591601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.308 × 10¹⁰¹(102-digit number)

43087638688199256115…49180601622769183201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

8.617 × 10¹⁰¹(102-digit number)

86175277376398512230…98361203245538366401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.723 × 10¹⁰²(103-digit number)

17235055475279702446…96722406491076732801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.447 × 10¹⁰²(103-digit number)

34470110950559404892…93444812982153465601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.894 × 10¹⁰²(103-digit number)

68940221901118809784…86889625964306931201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.378 × 10¹⁰³(104-digit number)

13788044380223761956…73779251928613862401

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