Block #305,050

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/11/2013, 6:43:24 AM · Difficulty 9.9935 · 6,505,015 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

9f7431fb99d0f83c0c86f2d6d542aa9bda3661a88a1268f068414c20bc95d334

View on Chainz ↗

Height

#305,050

Difficulty

9.993498

Transactions

Size

1.11 KB

Version

Bits

09fe55e4

Nonce

51,559

Timestamp

12/11/2013, 6:43:24 AM

Confirmations

6,505,015

Mined by

⛏️ aRAd9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

a11541a6fc27defaa15918b57a5714fd8e496a3627932b21f6a33b453515fc1d

Transactions (1)

Coinbasea11541a6fc27de…a33b453515fc1d

1 in → 29 out9.9800 XPM1.02 KB

Ad9pSzHt…cpJ3y2zz AYcLTeXR…bscgPops AMPANLy7…kkN5vWzv APeshfYV…3PKcKMKH ASWX42VM…XypQABkY

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.

2.229 × 10⁹³(94-digit number)

22298155376889539121…86650441286467525149

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

2.229 × 10⁹³(94-digit number)

22298155376889539121…86650441286467525149

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.459 × 10⁹³(94-digit number)

44596310753779078242…73300882572935050299

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.919 × 10⁹³(94-digit number)

89192621507558156484…46601765145870100599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.783 × 10⁹⁴(95-digit number)

17838524301511631296…93203530291740201199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.567 × 10⁹⁴(95-digit number)

35677048603023262593…86407060583480402399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.135 × 10⁹⁴(95-digit number)

71354097206046525187…72814121166960804799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.427 × 10⁹⁵(96-digit number)

14270819441209305037…45628242333921609599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.854 × 10⁹⁵(96-digit number)

28541638882418610075…91256484667843219199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.708 × 10⁹⁵(96-digit number)

57083277764837220150…82512969335686438399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.141 × 10⁹⁶(97-digit number)

11416655552967444030…65025938671372876799

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

Block #305,050

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