Block #430,318

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/5/2014, 10:29:04 AM · Difficulty 10.3412 · 6,375,390 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

dec0ba99e4f098c5737e92db0697e9b298b1d321d470b36d48a6b67b7134f658

View on Chainz ↗

Height

#430,318

Difficulty

10.341196

Transactions

Size

967 B

Version

Bits

0a5758a0

Nonce

1,088

Timestamp

3/5/2014, 10:29:04 AM

Confirmations

6,375,390

Mined by

⛏️ aSTPAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

c6ec5c984aa3b58e940381c07475d53e9fee7e763ef1f8a7c0504d7f5e7885ad

Transactions (1)

Coinbasec6ec5c984aa3b5…504d7f5e7885ad

1 in → 24 out9.3400 XPM878 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ANNg88pG…ppn21sTe

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.

3.372 × 10⁹¹(92-digit number)

33728370007886180621…11057344077563168001

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

3.372 × 10⁹¹(92-digit number)

33728370007886180621…11057344077563168001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.745 × 10⁹¹(92-digit number)

67456740015772361243…22114688155126336001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.349 × 10⁹²(93-digit number)

13491348003154472248…44229376310252672001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.698 × 10⁹²(93-digit number)

26982696006308944497…88458752620505344001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.396 × 10⁹²(93-digit number)

53965392012617888994…76917505241010688001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.079 × 10⁹³(94-digit number)

10793078402523577798…53835010482021376001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.158 × 10⁹³(94-digit number)

21586156805047155597…07670020964042752001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.317 × 10⁹³(94-digit number)

43172313610094311195…15340041928085504001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.634 × 10⁹³(94-digit number)

86344627220188622391…30680083856171008001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.726 × 10⁹⁴(95-digit number)

17268925444037724478…61360167712342016001

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