Block #373,943

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/24/2014, 3:55:00 PM · Difficulty 10.4272 · 6,420,589 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

4762f32ff943f08abc25ad7a294c1d869a295169485bfec9a8ad00c5b2006208

View on Chainz ↗

Height

#373,943

Difficulty

10.427198

Transactions

Size

2.87 KB

Version

Bits

0a6d5cd2

Nonce

34,951

Timestamp

1/24/2014, 3:55:00 PM

Confirmations

6,420,589

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

d48b61044bacc54f247b27ba1cca5276e3af776f2025509ff49359cb27958ae6

Transactions (2)

Coinbasef7da19f95331a8…264a984848cf7b

1 in → 1 out9.2100 XPM110 B

AeKNrjNj…1NEq95Ta

7a0b6b96c6ff68…f29315b65fb618

18 in → 2 out14.8020 XPM2.68 KB

AQQRAyeC…UDguko4W ALYZ5iVF…K5oi2R6d

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.

7.826 × 10⁹²(93-digit number)

78263253063653490654…79710758631221252159

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

7.826 × 10⁹²(93-digit number)

78263253063653490654…79710758631221252159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.565 × 10⁹³(94-digit number)

15652650612730698130…59421517262442504319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.130 × 10⁹³(94-digit number)

31305301225461396261…18843034524885008639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.261 × 10⁹³(94-digit number)

62610602450922792523…37686069049770017279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.252 × 10⁹⁴(95-digit number)

12522120490184558504…75372138099540034559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.504 × 10⁹⁴(95-digit number)

25044240980369117009…50744276199080069119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.008 × 10⁹⁴(95-digit number)

50088481960738234018…01488552398160138239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.001 × 10⁹⁵(96-digit number)

10017696392147646803…02977104796320276479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.003 × 10⁹⁵(96-digit number)

20035392784295293607…05954209592640552959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.007 × 10⁹⁵(96-digit number)

40070785568590587215…11908419185281105919

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