Block #286,481

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/30/2013, 10:12:06 PM · Difficulty 9.9856 · 6,509,077 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

7a73760911891958a4993674b2518cc95fa65a5b75096d4b2075c1357fe2e878

View on Chainz ↗

Height

#286,481

Difficulty

9.985614

Transactions

Size

1.11 KB

Version

Bits

09fc5131

Nonce

66,981

Timestamp

11/30/2013, 10:12:06 PM

Confirmations

6,509,077

Mined by

⛏️ _aRbAKde1i4dpqpgDtEArAY3oRXX8K88R1bw6g

Merkle Root

9856804a3ab00e8a785e4476593dd6a5682e8dd8c24bb5e255e993a3291830ce

Transactions (1)

Coinbase9856804a3ab00e…e993a3291830ce

1 in → 29 out9.9900 XPM1.02 KB

AKde1i4d…88R1bw6g Ad9pSzHt…cpJ3y2zz AJzWx2VD…j4ZSMit5 AcC2zSod…rtWatH79 AayReikY…2HAC42fs

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.

5.023 × 10⁹³(94-digit number)

50238809725537933414…55725822616709027839

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

5.023 × 10⁹³(94-digit number)

50238809725537933414…55725822616709027839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.004 × 10⁹⁴(95-digit number)

10047761945107586682…11451645233418055679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.009 × 10⁹⁴(95-digit number)

20095523890215173365…22903290466836111359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.019 × 10⁹⁴(95-digit number)

40191047780430346731…45806580933672222719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

8.038 × 10⁹⁴(95-digit number)

80382095560860693462…91613161867344445439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.607 × 10⁹⁵(96-digit number)

16076419112172138692…83226323734688890879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.215 × 10⁹⁵(96-digit number)

32152838224344277385…66452647469377781759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

6.430 × 10⁹⁵(96-digit number)

64305676448688554770…32905294938755563519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.286 × 10⁹⁶(97-digit number)

12861135289737710954…65810589877511127039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.572 × 10⁹⁶(97-digit number)

25722270579475421908…31621179755022254079

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