Block #54,085

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/16/2013, 6:38:04 PM · Difficulty 8.9301 · 6,741,210 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

2cbe7152db533ede7c27036bf0650b986bd2cb29c52d77b0ff246fb6d583b12a

View on Chainz ↗

Height

#54,085

Difficulty

8.930073

Transactions

Size

5.92 KB

Version

Bits

08ee1942

Nonce

Timestamp

7/16/2013, 6:38:04 PM

Confirmations

6,741,210

Mined by

⛏️ P2SHAPrz69KxtxTJwZ9iNSLWCU7184nKZQPBZb

Merkle Root

63d719633241aa6b351e7c3bb2c5a4b004908874e8875e9a94b2193604acb7f5

Transactions (2)

Coinbasee8d8d4eec275cf…99baabd71d8eee

1 in → 1 out12.5800 XPM110 B

APrz69Kx…nKZQPBZb

4dfe9624230ce2…412a837264f7bd

50 in → 1 out600.0000 XPM5.71 KB

AduwKP5J…wp1LyLxL

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.

2.990 × 10¹²⁰(121-digit number)

29907006029131432057…01745672178648255401

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

2.990 × 10¹²⁰(121-digit number)

29907006029131432057…01745672178648255401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.981 × 10¹²⁰(121-digit number)

59814012058262864114…03491344357296510801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.196 × 10¹²¹(122-digit number)

11962802411652572822…06982688714593021601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.392 × 10¹²¹(122-digit number)

23925604823305145645…13965377429186043201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.785 × 10¹²¹(122-digit number)

47851209646610291291…27930754858372086401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.570 × 10¹²¹(122-digit number)

95702419293220582583…55861509716744172801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.914 × 10¹²²(123-digit number)

19140483858644116516…11723019433488345601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.828 × 10¹²²(123-digit number)

38280967717288233033…23446038866976691201

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 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 8

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