Block #365,754

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/18/2014, 11:25:58 PM · Difficulty 10.4248 · 6,430,307 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

4cab503d30f0d032e7a97e2cc0d15a286b9a09d39d26c7af43b1e637bee2292a

View on Chainz ↗

Height

#365,754

Difficulty

10.424803

Transactions

Size

433 B

Version

Bits

0a6cbfde

Nonce

168,095

Timestamp

1/18/2014, 11:25:58 PM

Confirmations

6,430,307

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

ec11641396266406349ae9fec3e76318218abf40dda96d7ad7df5d1e3c27dd5b

Transactions (2)

Coinbasecea446af9da434…6e444d87f29eef

1 in → 1 out9.2100 XPM116 B

AbwWkWZt…kawDhufa

220828b5332210…76090b17256335

1 in → 2 out0.1900 XPM226 B

AVP53GXA…yb9MA2yX AUSmBVVb…ma4EhB1r

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.

1.225 × 10⁹⁸(99-digit number)

12259414906545472795…40628255639955333119

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

1.225 × 10⁹⁸(99-digit number)

12259414906545472795…40628255639955333119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.451 × 10⁹⁸(99-digit number)

24518829813090945590…81256511279910666239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.903 × 10⁹⁸(99-digit number)

49037659626181891181…62513022559821332479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.807 × 10⁹⁸(99-digit number)

98075319252363782363…25026045119642664959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.961 × 10⁹⁹(100-digit number)

19615063850472756472…50052090239285329919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.923 × 10⁹⁹(100-digit number)

39230127700945512945…00104180478570659839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.846 × 10⁹⁹(100-digit number)

78460255401891025891…00208360957141319679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.569 × 10¹⁰⁰(101-digit number)

15692051080378205178…00416721914282639359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.138 × 10¹⁰⁰(101-digit number)

31384102160756410356…00833443828565278719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

6.276 × 10¹⁰⁰(101-digit number)

62768204321512820712…01666887657130557439

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