Block #277,974

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/27/2013, 7:20:48 PM · Difficulty 9.9677 · 6,516,484 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

ddbccd3823a46aef68b595bc9155d44befbf133ef327ede727ca786619a02ff5

View on Chainz ↗

Height

#277,974

Difficulty

9.967676

Transactions

Size

767 B

Version

Bits

09f7b99f

Nonce

7,932

Timestamp

11/27/2013, 7:20:48 PM

Confirmations

6,516,484

Mined by

⛏️ =aRFAYckRkCFgTH4MEfpDbaimvV5cSTgDe5VSp

Merkle Root

3ecd3b146de3e8c29ae83eff0904941373f523793d5c4a832934d34977d70b22

Transactions (1)

Coinbase3ecd3b146de3e8…34d34977d70b22

1 in → 18 out10.0498 XPM675 B

AYckRkCF…TgDe5VSp AJzWx2VD…j4ZSMit5 AZ2pPuKg…95SN2Yr7 Ab3J4ipo…GaHrWuuW ASnheJmf…B3DBQmAG

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.

3.269 × 10¹⁰⁰(101-digit number)

32699202142483710469…70961143255763806241

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

3.269 × 10¹⁰⁰(101-digit number)

32699202142483710469…70961143255763806241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.539 × 10¹⁰⁰(101-digit number)

65398404284967420938…41922286511527612481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.307 × 10¹⁰¹(102-digit number)

13079680856993484187…83844573023055224961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.615 × 10¹⁰¹(102-digit number)

26159361713986968375…67689146046110449921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.231 × 10¹⁰¹(102-digit number)

52318723427973936751…35378292092220899841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.046 × 10¹⁰²(103-digit number)

10463744685594787350…70756584184441799681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.092 × 10¹⁰²(103-digit number)

20927489371189574700…41513168368883599361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.185 × 10¹⁰²(103-digit number)

41854978742379149400…83026336737767198721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.370 × 10¹⁰²(103-digit number)

83709957484758298801…66052673475534397441

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