Block #407,599

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/17/2014, 2:12:11 AM · Difficulty 10.4293 · 6,395,900 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

a0376455c4e1d1ed5263b04e738ef8e2a875cc9f808e642005a40fc87948e9b2

View on Chainz ↗

Height

#407,599

Difficulty

10.429338

Transactions

Size

901 B

Version

Bits

0a6de91a

Nonce

173,745

Timestamp

2/17/2014, 2:12:11 AM

Confirmations

6,395,900

Mined by

⛏️ 8aSoAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

968efe6ff9ebdb996381817d9c97c9f1b2cd815647b2400e9fc6256c156bb893

Transactions (1)

Coinbase968efe6ff9ebdb…c6256c156bb893

1 in → 22 out9.1800 XPM811 B

AQwRN8bE…V8PsTcY9 Aac9Hjdg…P4ktypc3 AGHJDQA6…hCLcZMXq AYtDvcGs…VuAcA7m7 AGKhfQo2…h7fBXLX6

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.

7.907 × 10⁹⁴(95-digit number)

79075677153049732809…03051378288805166079

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

7.907 × 10⁹⁴(95-digit number)

79075677153049732809…03051378288805166079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.581 × 10⁹⁵(96-digit number)

15815135430609946561…06102756577610332159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.163 × 10⁹⁵(96-digit number)

31630270861219893123…12205513155220664319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.326 × 10⁹⁵(96-digit number)

63260541722439786247…24411026310441328639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.265 × 10⁹⁶(97-digit number)

12652108344487957249…48822052620882657279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.530 × 10⁹⁶(97-digit number)

25304216688975914499…97644105241765314559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.060 × 10⁹⁶(97-digit number)

50608433377951828998…95288210483530629119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.012 × 10⁹⁷(98-digit number)

10121686675590365799…90576420967061258239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.024 × 10⁹⁷(98-digit number)

20243373351180731599…81152841934122516479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.048 × 10⁹⁷(98-digit number)

40486746702361463198…62305683868245032959

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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer