Block #340,674

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/2/2014, 10:55:45 PM · Difficulty 10.1324 · 6,458,480 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

a153ef1c79fc69f5a9f86d3bab1bb32a4469deee11b9078ae41782d983f71d08

View on Chainz ↗

Height

#340,674

Difficulty

10.132390

Transactions

Size

1.11 KB

Version

Bits

0a21e448

Nonce

88,205

Timestamp

1/2/2014, 10:55:45 PM

Confirmations

6,458,480

Mined by

⛏️ 2aRkAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

56356046a48a26e3871c0078e62116dd51cb4a9b2725859ffb455d8cc2a4b311

Transactions (1)

Coinbase56356046a48a26…455d8cc2a4b311

1 in → 29 out9.7100 XPM1.02 KB

AQwRN8bE…V8PsTcY9 AYtDvcGs…VuAcA7m7 AQ8QAT3J…rCFKuVbR AG5YAjec…VhA4Aeh1 AdDH1inU…KWPvb5kJ

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.

8.284 × 10⁹⁴(95-digit number)

82843733889172576489…51895064991801983999

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

8.284 × 10⁹⁴(95-digit number)

82843733889172576489…51895064991801983999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.656 × 10⁹⁵(96-digit number)

16568746777834515297…03790129983603967999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.313 × 10⁹⁵(96-digit number)

33137493555669030595…07580259967207935999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.627 × 10⁹⁵(96-digit number)

66274987111338061191…15160519934415871999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.325 × 10⁹⁶(97-digit number)

13254997422267612238…30321039868831743999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.650 × 10⁹⁶(97-digit number)

26509994844535224476…60642079737663487999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.301 × 10⁹⁶(97-digit number)

53019989689070448953…21284159475326975999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.060 × 10⁹⁷(98-digit number)

10603997937814089790…42568318950653951999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.120 × 10⁹⁷(98-digit number)

21207995875628179581…85136637901307903999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.241 × 10⁹⁷(98-digit number)

42415991751256359162…70273275802615807999

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