Block #430,389

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/5/2014, 11:31:27 AM · Difficulty 10.3423 · 6,368,505 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

ec9e7aee8fd1dc3326f91ea2e6fd509668770ea792b7f6c24994a0157eac8b98

View on Chainz ↗

Height

#430,389

Difficulty

10.342311

Transactions

Size

968 B

Version

Bits

0a57a1ad

Nonce

83,850

Timestamp

3/5/2014, 11:31:27 AM

Confirmations

6,368,505

Mined by

⛏️ 5aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

1efa46c6024c1061d9defd962e0c669d4f84160b2e3bc7bcdd7a5d38d8bf50f4

Transactions (1)

Coinbase1efa46c6024c10…7a5d38d8bf50f4

1 in → 24 out9.3300 XPM879 B

AQvZBsUo…hppgRZTJ AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 Ae7UyoY4…DtgAv9cY Aac9Hjdg…P4ktypc3

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.

1.253 × 10⁹³(94-digit number)

12539836299468149255…74778961632794097121

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

1.253 × 10⁹³(94-digit number)

12539836299468149255…74778961632794097121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.507 × 10⁹³(94-digit number)

25079672598936298510…49557923265588194241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.015 × 10⁹³(94-digit number)

50159345197872597020…99115846531176388481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.003 × 10⁹⁴(95-digit number)

10031869039574519404…98231693062352776961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.006 × 10⁹⁴(95-digit number)

20063738079149038808…96463386124705553921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.012 × 10⁹⁴(95-digit number)

40127476158298077616…92926772249411107841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

8.025 × 10⁹⁴(95-digit number)

80254952316596155232…85853544498822215681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.605 × 10⁹⁵(96-digit number)

16050990463319231046…71707088997644431361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.210 × 10⁹⁵(96-digit number)

32101980926638462093…43414177995288862721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

6.420 × 10⁹⁵(96-digit number)

64203961853276924186…86828355990577725441

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