Block #78,215

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/22/2013, 5:47:27 PM · Difficulty 9.2230 · 6,711,725 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

ad4b900107e31f8bb117b2fbe97316655735d9871b9e09e45d7bb1b4b95664e6

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Height

#78,215

Difficulty

9.223024

Transactions

Size

202 B

Version

Bits

09391821

Nonce

467

Timestamp

7/22/2013, 5:47:27 PM

Confirmations

6,711,725

Merkle Root

41888cb3bdcf345b2fb4969d9396ad56885363316e15a7df5aabb985ee54fe3e

Transactions (1)

Coinbase41888cb3bdcf34…abb985ee54fe3e

1 in → 1 out11.7400 XPM110 B

AK1JUKWL…oPR4rN5o

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.

5.789 × 10⁹⁹(100-digit number)

57894505821189197993…47706317661444301841

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

5.789 × 10⁹⁹(100-digit number)

57894505821189197993…47706317661444301841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.157 × 10¹⁰⁰(101-digit number)

11578901164237839598…95412635322888603681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.315 × 10¹⁰⁰(101-digit number)

23157802328475679197…90825270645777207361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.631 × 10¹⁰⁰(101-digit number)

46315604656951358394…81650541291554414721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

9.263 × 10¹⁰⁰(101-digit number)

92631209313902716789…63301082583108829441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.852 × 10¹⁰¹(102-digit number)

18526241862780543357…26602165166217658881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.705 × 10¹⁰¹(102-digit number)

37052483725561086715…53204330332435317761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.410 × 10¹⁰¹(102-digit number)

74104967451122173431…06408660664870635521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.482 × 10¹⁰²(103-digit number)

14820993490224434686…12817321329741271041

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