Block #349,283

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/8/2014, 8:10:33 AM · Difficulty 10.2695 · 6,447,601 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

2539636f823aed10cc4e9d944f74c9b9867e2ba08e8a986f5d4e20bc3b26ba6c

View on Chainz ↗

Height

#349,283

Difficulty

10.269452

Transactions

Size

1.05 KB

Version

Bits

0a44face

Nonce

50,779

Timestamp

1/8/2014, 8:10:33 AM

Confirmations

6,447,601

Mined by

⛏️ cTaRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

4f8c2d07a5334b1a89babff78c47bcc1f2fa26161417617c2a465bd3042b531e

Transactions (1)

Coinbase4f8c2d07a5334b…465bd3042b531e

1 in → 27 out9.4700 XPM981 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AZV4TwxQ…8JnQqSoH AKXeSXzu…yeuNjvhB

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.

3.000 × 10⁹⁶(97-digit number)

30000386546308754797…58453354824666945789

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

3.000 × 10⁹⁶(97-digit number)

30000386546308754797…58453354824666945789

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.000 × 10⁹⁶(97-digit number)

60000773092617509595…16906709649333891579

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.200 × 10⁹⁷(98-digit number)

12000154618523501919…33813419298667783159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.400 × 10⁹⁷(98-digit number)

24000309237047003838…67626838597335566319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.800 × 10⁹⁷(98-digit number)

48000618474094007676…35253677194671132639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.600 × 10⁹⁷(98-digit number)

96001236948188015352…70507354389342265279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.920 × 10⁹⁸(99-digit number)

19200247389637603070…41014708778684530559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.840 × 10⁹⁸(99-digit number)

38400494779275206141…82029417557369061119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.680 × 10⁹⁸(99-digit number)

76800989558550412282…64058835114738122239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.536 × 10⁹⁹(100-digit number)

15360197911710082456…28117670229476244479

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