Block #81,098

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/24/2013, 1:14:19 PM · Difficulty 9.2648 · 6,709,919 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

cb6ddef52a22822ef078e0a905e2632569213903c5810109fe622d8311fd67c5

View on Chainz ↗

Height

#81,098

Difficulty

9.264795

Transactions

Size

199 B

Version

Bits

0943c99c

Nonce

115,748

Timestamp

7/24/2013, 1:14:19 PM

Confirmations

6,709,919

Merkle Root

11fe9b616e6b0917939352e5060dca75182a82fd248db5b12cebd8f274fa0ff8

Transactions (1)

Coinbase11fe9b616e6b09…ebd8f274fa0ff8

1 in → 1 out11.6300 XPM109 B

ASUmFvxq…6mrDAKEZ

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.

3.194 × 10⁹³(94-digit number)

31940961580331411937…27700624007279386501

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

3.194 × 10⁹³(94-digit number)

31940961580331411937…27700624007279386501

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.388 × 10⁹³(94-digit number)

63881923160662823875…55401248014558773001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.277 × 10⁹⁴(95-digit number)

12776384632132564775…10802496029117546001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.555 × 10⁹⁴(95-digit number)

25552769264265129550…21604992058235092001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.110 × 10⁹⁴(95-digit number)

51105538528530259100…43209984116470184001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.022 × 10⁹⁵(96-digit number)

10221107705706051820…86419968232940368001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.044 × 10⁹⁵(96-digit number)

20442215411412103640…72839936465880736001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.088 × 10⁹⁵(96-digit number)

40884430822824207280…45679872931761472001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.176 × 10⁹⁵(96-digit number)

81768861645648414560…91359745863522944001

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