Block #430,525

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/5/2014, 1:34:00 PM · Difficulty 10.3441 · 6,373,017 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

2776a0d1c96262b56d125586af9621f120485116ffb258d6d2eaa21b8553755e

View on Chainz ↗

Height

#430,525

Difficulty

10.344075

Transactions

Size

424 B

Version

Bits

0a581548

Nonce

79,101

Timestamp

3/5/2014, 1:34:00 PM

Confirmations

6,373,017

Mined by

⛏️ P2SHAefNmfCCiMUgcSMoZqwmWZgc6ARj9JS3UM

Merkle Root

b8b1641d4e1461362ea75953f300e5dc9282d90809a3c4419bd5e204c1208c4b

Transactions (2)

Coinbase2f2336bdc3f719…6667aebd2604f3

1 in → 1 out9.3400 XPM109 B

AefNmfCC…Rj9JS3UM

d64fa22ce2c2f0…b116c7490dbbd3

1 in → 2 out2.6029 XPM226 B

AXEitfKT…nEgPPnQZ ANCeLjWG…rf6VdgHx

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.

1.529 × 10⁹³(94-digit number)

15299617093621759494…10878755702927576641

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

1.529 × 10⁹³(94-digit number)

15299617093621759494…10878755702927576641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.059 × 10⁹³(94-digit number)

30599234187243518988…21757511405855153281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.119 × 10⁹³(94-digit number)

61198468374487037976…43515022811710306561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.223 × 10⁹⁴(95-digit number)

12239693674897407595…87030045623420613121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.447 × 10⁹⁴(95-digit number)

24479387349794815190…74060091246841226241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.895 × 10⁹⁴(95-digit number)

48958774699589630380…48120182493682452481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.791 × 10⁹⁴(95-digit number)

97917549399179260761…96240364987364904961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.958 × 10⁹⁵(96-digit number)

19583509879835852152…92480729974729809921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.916 × 10⁹⁵(96-digit number)

39167019759671704304…84961459949459619841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

7.833 × 10⁹⁵(96-digit number)

78334039519343408609…69922919898919239681

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