Block #215,473

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/18/2013, 2:46:44 AM · Difficulty 9.9255 · 6,583,092 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

f4ddb8c134474e1ad9ce0265deabde91f7f98b8cd70a20edfd797f1bd1a8bd79

View on Chainz ↗

Height

#215,473

Difficulty

9.925485

Transactions

Size

4.80 KB

Version

Bits

09ecec9d

Nonce

1,164,745,691

Timestamp

10/18/2013, 2:46:44 AM

Confirmations

6,583,092

Mined by

⛏️ IR`Aa6xA9KKXE28Z3gorJHZ3FtBVGo7woWzPm

Merkle Root

ef49486208f0f6844f4be311c029d71bfe8f160eef0a0f5705c6b8a144aedd51

Transactions (1)

Coinbaseef49486208f0f6…c6b8a144aedd51

1 in → 140 out10.0900 XPM4.71 KB

Aa6xA9KK…o7woWzPm AGBW7BWm…nG9vK5UT AWgwrQ5r…KVAzQwZ1 AenoL7Bk…DtRssSvW AdL4ZZDR…2eQtg1T9

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.

7.183 × 10⁹⁷(98-digit number)

71839346436678692944…57136805824566496001

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

7.183 × 10⁹⁷(98-digit number)

71839346436678692944…57136805824566496001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.436 × 10⁹⁸(99-digit number)

14367869287335738588…14273611649132992001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.873 × 10⁹⁸(99-digit number)

28735738574671477177…28547223298265984001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

5.747 × 10⁹⁸(99-digit number)

57471477149342954355…57094446596531968001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.149 × 10⁹⁹(100-digit number)

11494295429868590871…14188893193063936001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.298 × 10⁹⁹(100-digit number)

22988590859737181742…28377786386127872001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.597 × 10⁹⁹(100-digit number)

45977181719474363484…56755572772255744001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

9.195 × 10⁹⁹(100-digit number)

91954363438948726968…13511145544511488001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.839 × 10¹⁰⁰(101-digit number)

18390872687789745393…27022291089022976001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.678 × 10¹⁰⁰(101-digit number)

36781745375579490787…54044582178045952001

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