Block #436,024

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/9/2014, 8:11:50 AM · Difficulty 10.3549 · 6,355,463 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

779bcf62e536462f7d5ee84355a55a9d5159c6510649c9132e3d37f3fe2f17ee

View on Chainz ↗

Height

#436,024

Difficulty

10.354860

Transactions

Size

597 B

Version

Bits

0a5ad81f

Nonce

703,663

Timestamp

3/9/2014, 8:11:50 AM

Confirmations

6,355,463

Merkle Root

ca6bdf5383b58a96c3df41638aa6d5ee64fdf53d3f284808e25e62bae5f70683

Transactions (2)

Coinbasebd2d2bf19a8082…d4a0e0716e13de

1 in → 1 out9.3200 XPM110 B

AeKNrjNj…1NEq95Ta

f71f5cfc79d281…7c109bc1e39b45

1 in → 7 out20.2806 XPM396 B

ARa1Wtst…381uiFDJ AXrzXb7L…U8tkq3aK AXX7cAvF…GKagXkZm AWLPmFpg…2Wt1W7zg Ad93oqV8…4c3TiQK5

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.

1.398 × 10⁹⁷(98-digit number)

13981150921693253606…22835057199463608321

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

1.398 × 10⁹⁷(98-digit number)

13981150921693253606…22835057199463608321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.796 × 10⁹⁷(98-digit number)

27962301843386507212…45670114398927216641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.592 × 10⁹⁷(98-digit number)

55924603686773014425…91340228797854433281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.118 × 10⁹⁸(99-digit number)

11184920737354602885…82680457595708866561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.236 × 10⁹⁸(99-digit number)

22369841474709205770…65360915191417733121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.473 × 10⁹⁸(99-digit number)

44739682949418411540…30721830382835466241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

8.947 × 10⁹⁸(99-digit number)

89479365898836823080…61443660765670932481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.789 × 10⁹⁹(100-digit number)

17895873179767364616…22887321531341864961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.579 × 10⁹⁹(100-digit number)

35791746359534729232…45774643062683729921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

7.158 × 10⁹⁹(100-digit number)

71583492719069458464…91549286125367459841

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