Block #262,479

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/16/2013, 9:38:12 PM · Difficulty 9.9685 · 6,545,109 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f494ed30835f6f4ec9a6fd71f8d48656be66b9e5ee7f5cb08005398e281c43bc

View on Chainz ↗

Height

#262,479

Difficulty

9.968544

Transactions

Size

1.61 KB

Version

Bits

09f7f27e

Nonce

76,586

Timestamp

11/16/2013, 9:38:12 PM

Confirmations

6,545,109

Mined by

⛏️ OaR2AKXeSXzuNp3rXfbvqBPuAUeHUgyeuNjvhB

Merkle Root

0d38755bee7209d97cb59dcda1ff08a8d2ae41062a0bf8678f853a00ed28ec2b

Transactions (1)

Coinbase0d38755bee7209…853a00ed28ec2b

1 in → 44 out10.0300 XPM1.52 KB

AKXeSXzu…yeuNjvhB AXtCwBuV…cnbwWtbY AQapNBe8…Pxk4vkev AQtzUSwq…htAuF3yC AUSGA5VC…GYHbnJtz

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.

2.572 × 10⁹³(94-digit number)

25722328437540299277…94312036429563922319

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

2.572 × 10⁹³(94-digit number)

25722328437540299277…94312036429563922319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.144 × 10⁹³(94-digit number)

51444656875080598555…88624072859127844639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.028 × 10⁹⁴(95-digit number)

10288931375016119711…77248145718255689279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.057 × 10⁹⁴(95-digit number)

20577862750032239422…54496291436511378559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.115 × 10⁹⁴(95-digit number)

41155725500064478844…08992582873022757119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.231 × 10⁹⁴(95-digit number)

82311451000128957688…17985165746045514239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.646 × 10⁹⁵(96-digit number)

16462290200025791537…35970331492091028479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.292 × 10⁹⁵(96-digit number)

32924580400051583075…71940662984182056959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.584 × 10⁹⁵(96-digit number)

65849160800103166151…43881325968364113919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.316 × 10⁹⁶(97-digit number)

13169832160020633230…87762651936728227839

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 #262,479

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