Block #243,849

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/4/2013, 12:50:36 PM · Difficulty 9.9621 · 6,560,346 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

9e5e0aed753da55c51642bf9e7de81a02f537ac3721b74c749713fbf4113919b

View on Chainz ↗

Height

#243,849

Difficulty

9.962123

Transactions

Size

1.81 KB

Version

Bits

09f64db5

Nonce

66,242

Timestamp

11/4/2013, 12:50:36 PM

Confirmations

6,560,346

Mined by

⛏️ Rw7ARpndEmcGyFUFhdFVbgqJiPBAmHg792kEk

Merkle Root

196ed372844589c7ef3a16429e7790f8e4463803fc5d3eab7e84d4e558c1854d

Transactions (1)

Coinbase196ed372844589…84d4e558c1854d

1 in → 50 out10.0400 XPM1.72 KB

ARpndEmc…Hg792kEk AeZmMFY8…mjAy5Mi4 AdL4ZZDR…2eQtg1T9 AQtzUSwq…htAuF3yC AaKnhCXG…njJfrbew

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.

6.209 × 10⁹²(93-digit number)

62094433370536829829…96243718673697553051

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

6.209 × 10⁹²(93-digit number)

62094433370536829829…96243718673697553051

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.241 × 10⁹³(94-digit number)

12418886674107365965…92487437347395106101

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.483 × 10⁹³(94-digit number)

24837773348214731931…84974874694790212201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.967 × 10⁹³(94-digit number)

49675546696429463863…69949749389580424401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

9.935 × 10⁹³(94-digit number)

99351093392858927726…39899498779160848801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.987 × 10⁹⁴(95-digit number)

19870218678571785545…79798997558321697601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.974 × 10⁹⁴(95-digit number)

39740437357143571090…59597995116643395201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.948 × 10⁹⁴(95-digit number)

79480874714287142181…19195990233286790401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.589 × 10⁹⁵(96-digit number)

15896174942857428436…38391980466573580801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.179 × 10⁹⁵(96-digit number)

31792349885714856872…76783960933147161601

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