Block #63,665

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/19/2013, 2:54:33 AM · Difficulty 8.9798 · 6,731,097 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

5dbe4cc3abcabab49bda468b603cbf29b89e2450d5fc38f6e7d686fc7da39e77

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Height

#63,665

Difficulty

8.979751

Transactions

Size

206 B

Version

Bits

08fad0f0

Nonce

Timestamp

7/19/2013, 2:54:33 AM

Confirmations

6,731,097

Mined by

⛏️ P2SHAGY4TBx7s42EHEAbrwoVx7JoxEYfD8h7Va

Merkle Root

bdc9f431e6091b1e473d7525254e4717fb929bffa6b98724346748b686b096a9

Transactions (1)

Coinbasebdc9f431e6091b…6748b686b096a9

1 in → 1 out12.3800 XPM110 B

AGY4TBx7…YfD8h7Va

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.

6.611 × 10¹⁰⁸(109-digit number)

66112141575280140162…60518234140511703401

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

6.611 × 10¹⁰⁸(109-digit number)

66112141575280140162…60518234140511703401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.322 × 10¹⁰⁹(110-digit number)

13222428315056028032…21036468281023406801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.644 × 10¹⁰⁹(110-digit number)

26444856630112056065…42072936562046813601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

5.288 × 10¹⁰⁹(110-digit number)

52889713260224112130…84145873124093627201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.057 × 10¹¹⁰(111-digit number)

10577942652044822426…68291746248187254401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.115 × 10¹¹⁰(111-digit number)

21155885304089644852…36583492496374508801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.231 × 10¹¹⁰(111-digit number)

42311770608179289704…73166984992749017601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

8.462 × 10¹¹⁰(111-digit number)

84623541216358579408…46333969985498035201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.692 × 10¹¹¹(112-digit number)

16924708243271715881…92667939970996070401

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