Block #408,868

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/17/2014, 11:50:15 PM · Difficulty 10.4246 · 6,387,226 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

49ffba9cd7a5f9818d77359efb2df1698530c6371e0a8a83718aed1d797e8077

View on Chainz ↗

Height

#408,868

Difficulty

10.424624

Transactions

Size

969 B

Version

Bits

0a6cb430

Nonce

282,836

Timestamp

2/17/2014, 11:50:15 PM

Confirmations

6,387,226

Mined by

⛏️ $=aSrAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

279e891083959cfb4e488989c2976c46ed5cc847b3ecb3a9aa3e0d570d82fe5c

Transactions (1)

Coinbase279e891083959c…3e0d570d82fe5c

1 in → 24 out9.1900 XPM879 B

AQwRN8bE…V8PsTcY9 Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AGKhfQo2…h7fBXLX6 AQvZBsUo…hppgRZTJ

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.

1.235 × 10⁹⁴(95-digit number)

12359394203663444545…42903053795166643201

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

1.235 × 10⁹⁴(95-digit number)

12359394203663444545…42903053795166643201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.471 × 10⁹⁴(95-digit number)

24718788407326889091…85806107590333286401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.943 × 10⁹⁴(95-digit number)

49437576814653778182…71612215180666572801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.887 × 10⁹⁴(95-digit number)

98875153629307556364…43224430361333145601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.977 × 10⁹⁵(96-digit number)

19775030725861511272…86448860722666291201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.955 × 10⁹⁵(96-digit number)

39550061451723022545…72897721445332582401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.910 × 10⁹⁵(96-digit number)

79100122903446045091…45795442890665164801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.582 × 10⁹⁶(97-digit number)

15820024580689209018…91590885781330329601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.164 × 10⁹⁶(97-digit number)

31640049161378418036…83181771562660659201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

6.328 × 10⁹⁶(97-digit number)

63280098322756836073…66363543125321318401

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