Block #24,878

2CCLength 7★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/13/2013, 12:23:52 AM · Difficulty 7.9681 · 6,765,092 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

c49ef90bc77ecb552f95839feb7a29e3ba3f52a76f49ece01f11641108b014d0

View on Chainz ↗

Height

#24,878

Difficulty

7.968060

Transactions

Size

535 B

Version

Bits

07f7d2c8

Nonce

484

Timestamp

7/13/2013, 12:23:52 AM

Confirmations

6,765,092

Merkle Root

1355f6f6fd213f24a4f5e0502b8885046ad8b36670687a1dfe5e56ba373006b7

Transactions (2)

Coinbasede944e4c022b9c…32eea25c1c94ce

1 in → 1 out15.7400 XPM108 B

AV3Mx3Aq…AKiwER2W

b65795bac83c64…2dd9b9607e0be8

2 in → 2 out30.0600 XPM339 B

ARtDMbCU…WiPkYAii AKoTrjJc…rQX8kNEz

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.

1.180 × 10⁹⁰(91-digit number)

11808985209714913046…24698551031408459121

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

1.180 × 10⁹⁰(91-digit number)

11808985209714913046…24698551031408459121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.361 × 10⁹⁰(91-digit number)

23617970419429826092…49397102062816918241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.723 × 10⁹⁰(91-digit number)

47235940838859652184…98794204125633836481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.447 × 10⁹⁰(91-digit number)

94471881677719304368…97588408251267672961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.889 × 10⁹¹(92-digit number)

18894376335543860873…95176816502535345921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.778 × 10⁹¹(92-digit number)

37788752671087721747…90353633005070691841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.557 × 10⁹¹(92-digit number)

75577505342175443494…80707266010141383681

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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