Block #252,673

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/9/2013, 5:23:37 PM · Difficulty 9.9714 · 6,538,459 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

4781eea727b9155598f89f10b09ad81850e3b192e37660354200e79842eccf12

View on Chainz ↗

Height

#252,673

Difficulty

9.971350

Transactions

Size

2.11 KB

Version

Bits

09f8aa68

Nonce

235,708

Timestamp

11/9/2013, 5:23:37 PM

Confirmations

6,538,459

Merkle Root

4c13c4dd62471dc31cc6b5f8526683f219b9b60e0dc0ac96d70ba85675c41f06

Transactions (1)

Coinbase4c13c4dd62471d…0ba85675c41f06

1 in → 59 out10.0100 XPM2.02 KB

ANmq3Nzr…5xhpaHfG AFqKfjez…qX9Ace3g AKtK4SH7…Ti8JpB2W AQtzUSwq…htAuF3yC AScCYXya…oAz38X3p

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.

2.424 × 10⁹¹(92-digit number)

24244386816723418927…41223195163319869441

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

2.424 × 10⁹¹(92-digit number)

24244386816723418927…41223195163319869441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.848 × 10⁹¹(92-digit number)

48488773633446837855…82446390326639738881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.697 × 10⁹¹(92-digit number)

96977547266893675710…64892780653279477761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.939 × 10⁹²(93-digit number)

19395509453378735142…29785561306558955521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.879 × 10⁹²(93-digit number)

38791018906757470284…59571122613117911041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.758 × 10⁹²(93-digit number)

77582037813514940568…19142245226235822081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.551 × 10⁹³(94-digit number)

15516407562702988113…38284490452471644161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.103 × 10⁹³(94-digit number)

31032815125405976227…76568980904943288321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.206 × 10⁹³(94-digit number)

62065630250811952454…53137961809886576641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.241 × 10⁹⁴(95-digit number)

12413126050162390490…06275923619773153281

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