Block #345,247

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/5/2014, 7:26:50 PM · Difficulty 10.2097 · 6,451,427 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f815e6572b6026bd3dd3f5c9d82ea7fdab96724451d8436c53bf344d03b591a7

View on Chainz ↗

Height

#345,247

Difficulty

10.209735

Transactions

Size

1.08 KB

Version

Bits

0a35b12a

Nonce

10,517

Timestamp

1/5/2014, 7:26:50 PM

Confirmations

6,451,427

Mined by

⛏️ DaRzAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

39db80a35ebb4aac190b750250e85c34d9f95b85ae47b39dc743441ad1d1d021

Transactions (1)

Coinbase39db80a35ebb4a…43441ad1d1d021

1 in → 28 out9.5600 XPM1015 B

AQwRN8bE…V8PsTcY9 AZemWJAo…6jhDtieG AYtDvcGs…VuAcA7m7 AQ8QAT3J…rCFKuVbR Ad9pSzHt…cpJ3y2zz

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.

1.940 × 10⁹³(94-digit number)

19403312596301227281…42825644093332455519

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

1.940 × 10⁹³(94-digit number)

19403312596301227281…42825644093332455519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.880 × 10⁹³(94-digit number)

38806625192602454562…85651288186664911039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

7.761 × 10⁹³(94-digit number)

77613250385204909124…71302576373329822079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.552 × 10⁹⁴(95-digit number)

15522650077040981824…42605152746659644159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.104 × 10⁹⁴(95-digit number)

31045300154081963649…85210305493319288319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.209 × 10⁹⁴(95-digit number)

62090600308163927299…70420610986638576639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.241 × 10⁹⁵(96-digit number)

12418120061632785459…40841221973277153279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.483 × 10⁹⁵(96-digit number)

24836240123265570919…81682443946554306559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.967 × 10⁹⁵(96-digit number)

49672480246531141839…63364887893108613119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

9.934 × 10⁹⁵(96-digit number)

99344960493062283679…26729775786217226239

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