Block #277,994

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/27/2013, 7:31:26 PM · Difficulty 9.9677 · 6,515,582 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

a2261c5401a2c84fcc1cb7f6174293bdf4cfe01ef8709755c2aacf51d5defb37

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Height

#277,994

Difficulty

9.967738

Transactions

Size

1.15 KB

Version

Bits

09f7bdb2

Nonce

2,520

Timestamp

11/27/2013, 7:31:26 PM

Confirmations

6,515,582

Merkle Root

f9e0cf22419e883179027ce9deb29b9f24297a5907afd8b0baad96dbb8a28c8f

Transactions (1)

Coinbasef9e0cf22419e88…ad96dbb8a28c8f

1 in → 30 out10.0300 XPM1.06 KB

AbiApRgN…g8QuFUwL Abv8pzf1…t4zPXDTV AWA5FEzr…x9RdPKTy AJaJmdSN…aEQRPkyF ARpndEmc…Hg792kEk

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.

3.715 × 10⁹³(94-digit number)

37151082979017926991…69076160123472896001

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

3.715 × 10⁹³(94-digit number)

37151082979017926991…69076160123472896001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

7.430 × 10⁹³(94-digit number)

74302165958035853983…38152320246945792001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.486 × 10⁹⁴(95-digit number)

14860433191607170796…76304640493891584001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.972 × 10⁹⁴(95-digit number)

29720866383214341593…52609280987783168001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.944 × 10⁹⁴(95-digit number)

59441732766428683186…05218561975566336001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.188 × 10⁹⁵(96-digit number)

11888346553285736637…10437123951132672001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.377 × 10⁹⁵(96-digit number)

23776693106571473274…20874247902265344001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.755 × 10⁹⁵(96-digit number)

47553386213142946549…41748495804530688001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

9.510 × 10⁹⁵(96-digit number)

95106772426285893098…83496991609061376001

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