Block #474,988

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/4/2014, 10:38:07 PM · Difficulty 10.4551 · 6,328,825 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

2453d1525a7b48a57348644a1a81369cb7821cd56a1637caf85c44396106cb61

View on Chainz ↗

Height

#474,988

Difficulty

10.455147

Transactions

Size

936 B

Version

Bits

0a748487

Nonce

240,746

Timestamp

4/4/2014, 10:38:07 PM

Confirmations

6,328,825

Mined by

⛏️ l?AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

84c4c5a9891dcaeb56acd957e14ddec23da372c1872e9fb485197ab599233370

Transactions (1)

Coinbase84c4c5a9891dca…197ab599233370

1 in → 23 out9.1300 XPM845 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw Adbb4svj…dQWTHsq5 AMW1p9oT…2TzdaZxH AUFKXvnz…342ApNcm

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.

7.982 × 10⁹⁶(97-digit number)

79821303595432808904…49702455574045667459

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

7.982 × 10⁹⁶(97-digit number)

79821303595432808904…49702455574045667459

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.596 × 10⁹⁷(98-digit number)

15964260719086561780…99404911148091334919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.192 × 10⁹⁷(98-digit number)

31928521438173123561…98809822296182669839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.385 × 10⁹⁷(98-digit number)

63857042876346247123…97619644592365339679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.277 × 10⁹⁸(99-digit number)

12771408575269249424…95239289184730679359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.554 × 10⁹⁸(99-digit number)

25542817150538498849…90478578369461358719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.108 × 10⁹⁸(99-digit number)

51085634301076997698…80957156738922717439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.021 × 10⁹⁹(100-digit number)

10217126860215399539…61914313477845434879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.043 × 10⁹⁹(100-digit number)

20434253720430799079…23828626955690869759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.086 × 10⁹⁹(100-digit number)

40868507440861598159…47657253911381739519

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