Block #365,093

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/18/2014, 12:32:54 PM · Difficulty 10.4232 · 6,437,961 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

83f85e7d28f9b92b4ca2d3710a9050bbfdbdfea2c35aa3c839534810930f9949

View on Chainz ↗

Height

#365,093

Difficulty

10.423234

Transactions

Size

766 B

Version

Bits

0a6c5912

Nonce

931

Timestamp

1/18/2014, 12:32:54 PM

Confirmations

6,437,961

Mined by

⛏️ %FAM4c6u8dYeQBkdo3RbtZ8WqY8DwUNSLEd4

Merkle Root

f3bfb4a8eb34a52eba7d6df7323667d843125d1464215d59432de2f3612b118e

Transactions (1)

Coinbasef3bfb4a8eb34a5…2de2f3612b118e

1 in → 18 out9.1900 XPM675 B

AM4c6u8d…wUNSLEd4 AFutDVqJ…TJTJj6UF APFsQ3Fo…xoFKrF12 AaJwNkvB…uqCwyjYa AL2a2TYD…f9sjcukW

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.

6.629 × 10⁹⁶(97-digit number)

66298652130913081228…65415915016121801439

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

6.629 × 10⁹⁶(97-digit number)

66298652130913081228…65415915016121801439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.325 × 10⁹⁷(98-digit number)

13259730426182616245…30831830032243602879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.651 × 10⁹⁷(98-digit number)

26519460852365232491…61663660064487205759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.303 × 10⁹⁷(98-digit number)

53038921704730464982…23327320128974411519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.060 × 10⁹⁸(99-digit number)

10607784340946092996…46654640257948823039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.121 × 10⁹⁸(99-digit number)

21215568681892185992…93309280515897646079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.243 × 10⁹⁸(99-digit number)

42431137363784371985…86618561031795292159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.486 × 10⁹⁸(99-digit number)

84862274727568743971…73237122063590584319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.697 × 10⁹⁹(100-digit number)

16972454945513748794…46474244127181168639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.394 × 10⁹⁹(100-digit number)

33944909891027497588…92948488254362337279

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