Block #44,660

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/15/2013, 12:20:14 AM · Difficulty 8.7252 · 6,750,339 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

8e52d573caad6f99ac560578c661ec25a94e5b48c08185c6ad7e0b6c6549006c

View on Chainz ↗

Height

#44,660

Difficulty

8.725165

Transactions

Size

4.74 KB

Version

Bits

08b9a465

Nonce

707

Timestamp

7/15/2013, 12:20:14 AM

Confirmations

6,750,339

Mined by

⛏️ P2SHAajP5ZVUVnvhhfshpYE6KZDLXUYAv14Zbk

Merkle Root

dccda435224619dc8122eb6719c736d63190622e092f03eac9d37cdd975fd9c1

Transactions (3)

Coinbased0feb71a808759…e0519b38d7087d

1 in → 1 out13.1800 XPM110 B

AajP5ZVU…YAv14Zbk

268ccdfa6ec5e0…c56f58cae5e6de

3 in → 1 out46.9100 XPM386 B

Acs9SHrk…QJSB8SFG

2107bd771c4d38…a1d09677a97ec7

37 in → 1 out560.0000 XPM4.16 KB

ARsrDwcp…Fv5SKr8Y

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.

5.486 × 10⁹⁶(97-digit number)

54866696854651218417…81872169027096654401

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

5.486 × 10⁹⁶(97-digit number)

54866696854651218417…81872169027096654401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.097 × 10⁹⁷(98-digit number)

10973339370930243683…63744338054193308801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.194 × 10⁹⁷(98-digit number)

21946678741860487367…27488676108386617601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.389 × 10⁹⁷(98-digit number)

43893357483720974734…54977352216773235201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

8.778 × 10⁹⁷(98-digit number)

87786714967441949468…09954704433546470401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.755 × 10⁹⁸(99-digit number)

17557342993488389893…19909408867092940801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.511 × 10⁹⁸(99-digit number)

35114685986976779787…39818817734185881601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.022 × 10⁹⁸(99-digit number)

70229371973953559574…79637635468371763201

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