Block #432,680

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/7/2014, 2:11:09 AM · Difficulty 10.3393 · 6,366,591 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

24aee374f318e327779151cd4aa1e333269d1a4c053e48c2151539c02b38c20a

View on Chainz ↗

Height

#432,680

Difficulty

10.339333

Transactions

Size

1.04 KB

Version

Bits

0a56de8f

Nonce

1,097

Timestamp

3/7/2014, 2:11:09 AM

Confirmations

6,366,591

Mined by

⛏️ aS*.Aac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

496265acfc6472e137e4cd1f6143fd4face4084905756d99acbadbed9aae541c

Transactions (1)

Coinbase496265acfc6472…badbed9aae541c

1 in → 27 out9.3400 XPM981 B

Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AMm3qeod…8PBiCMXU

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.

1.318 × 10⁹²(93-digit number)

13189648675835877974…66419369783063736401

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

1.318 × 10⁹²(93-digit number)

13189648675835877974…66419369783063736401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.637 × 10⁹²(93-digit number)

26379297351671755948…32838739566127472801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.275 × 10⁹²(93-digit number)

52758594703343511897…65677479132254945601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.055 × 10⁹³(94-digit number)

10551718940668702379…31354958264509891201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.110 × 10⁹³(94-digit number)

21103437881337404759…62709916529019782401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.220 × 10⁹³(94-digit number)

42206875762674809518…25419833058039564801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

8.441 × 10⁹³(94-digit number)

84413751525349619036…50839666116079129601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.688 × 10⁹⁴(95-digit number)

16882750305069923807…01679332232158259201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.376 × 10⁹⁴(95-digit number)

33765500610139847614…03358664464316518401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

6.753 × 10⁹⁴(95-digit number)

67531001220279695228…06717328928633036801

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