Block #374,155

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/24/2014, 7:39:22 PM · Difficulty 10.4260 · 6,417,671 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

37a520704dbd5b6caa03801e2fda112f3cb6c3e81f192a5b76fa75ede0ab52ad

View on Chainz ↗

Height

#374,155

Difficulty

10.426016

Transactions

Size

893 B

Version

Bits

0a6d0f5d

Nonce

988,307

Timestamp

1/24/2014, 7:39:22 PM

Confirmations

6,417,671

Merkle Root

b53d6bab6b5fefbec5b3c3ee3919eb98a726ff82519e90a9d5994f00e3b2f960

Transactions (2)

Coinbase2645aefa28b2a7…44679df2602d94

1 in → 1 out9.2000 XPM110 B

AeKNrjNj…1NEq95Ta

3e1a3d73f39f11…b140aee5dca4e8

3 in → 10 out27.5200 XPM692 B

AeKNrjNj…1NEq95Ta ASHs3BR3…HuFA7Lpt AV9HNKoF…quJ6NzEn AFw4uFDH…ykrLVsJg AGdMTtTY…haTFjuGh

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.

5.958 × 10⁹⁶(97-digit number)

59584130970256336465…48807538681931680641

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

5.958 × 10⁹⁶(97-digit number)

59584130970256336465…48807538681931680641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.191 × 10⁹⁷(98-digit number)

11916826194051267293…97615077363863361281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.383 × 10⁹⁷(98-digit number)

23833652388102534586…95230154727726722561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.766 × 10⁹⁷(98-digit number)

47667304776205069172…90460309455453445121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

9.533 × 10⁹⁷(98-digit number)

95334609552410138345…80920618910906890241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.906 × 10⁹⁸(99-digit number)

19066921910482027669…61841237821813780481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.813 × 10⁹⁸(99-digit number)

38133843820964055338…23682475643627560961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.626 × 10⁹⁸(99-digit number)

76267687641928110676…47364951287255121921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.525 × 10⁹⁹(100-digit number)

15253537528385622135…94729902574510243841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.050 × 10⁹⁹(100-digit number)

30507075056771244270…89459805149020487681

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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