Block #465,433

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/29/2014, 11:05:15 AM · Difficulty 10.4252 · 6,324,537 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

42532ff6a330b918a36f397c3a0f8124feeeabd6b10168adb9471e4a87817fd0

View on Chainz ↗

Height

#465,433

Difficulty

10.425216

Transactions

Size

640 B

Version

Bits

0a6cdaed

Nonce

3,523,190

Timestamp

3/29/2014, 11:05:15 AM

Confirmations

6,324,537

Merkle Root

80ff7a0b2471b972ce03fa846628e653b5a3411622cb9b31a534e1753c528d60

Transactions (2)

Coinbase1c3a2aeb0d7164…8ccb877f64e485

1 in → 1 out9.2000 XPM109 B

Ad1aWLvY…Pc8cALJB

620f3d338d9950…6b4fa93450bf49

2 in → 6 out18.4400 XPM440 B

AbegGsha…RYQxrpFP AVrD6maY…W77cdqzz AeR5xAAu…QS19drpA Ab1YTAY5…9zZqa2sB AeKNrjNj…1NEq95Ta

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.

3.378 × 10⁹⁶(97-digit number)

33782980528925750118…81474680468553344001

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

3.378 × 10⁹⁶(97-digit number)

33782980528925750118…81474680468553344001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.756 × 10⁹⁶(97-digit number)

67565961057851500237…62949360937106688001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.351 × 10⁹⁷(98-digit number)

13513192211570300047…25898721874213376001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.702 × 10⁹⁷(98-digit number)

27026384423140600094…51797443748426752001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.405 × 10⁹⁷(98-digit number)

54052768846281200189…03594887496853504001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.081 × 10⁹⁸(99-digit number)

10810553769256240037…07189774993707008001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.162 × 10⁹⁸(99-digit number)

21621107538512480075…14379549987414016001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.324 × 10⁹⁸(99-digit number)

43242215077024960151…28759099974828032001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.648 × 10⁹⁸(99-digit number)

86484430154049920303…57518199949656064001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.729 × 10⁹⁹(100-digit number)

17296886030809984060…15036399899312128001

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