Block #291,709

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/3/2013, 8:08:37 AM · Difficulty 9.9900 · 6,512,076 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

df12698aceae8e7f5aab24baddaebe1e95c19c5f640520c29436c232fd19adc9

View on Chainz ↗

Height

#291,709

Difficulty

9.989985

Transactions

Size

866 B

Version

Bits

09fd6fa6

Nonce

57,038

Timestamp

12/3/2013, 8:08:37 AM

Confirmations

6,512,076

Mined by

⛏️ P2SHAN3ZV4id3nUvqT83WDX6B4whBQHnoGhFJS

Merkle Root

a95210998564a9a34fdfcd129ace725deea5986bf3df8d2b096026ea3abb4c35

Transactions (2)

Coinbasec0cec0ea30bceb…35efadbcd54436

1 in → 1 out10.0200 XPM109 B

AN3ZV4id…HnoGhFJS

670288a5166393…323ca3288883fb

4 in → 2 out26.6470 XPM668 B

APMctEQY…qbiUpFkf AdfUfdKA…2FVj9TPE

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.

2.413 × 10⁹³(94-digit number)

24132023873210299327…70561347936184145279

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

2.413 × 10⁹³(94-digit number)

24132023873210299327…70561347936184145279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.826 × 10⁹³(94-digit number)

48264047746420598654…41122695872368290559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

9.652 × 10⁹³(94-digit number)

96528095492841197309…82245391744736581119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.930 × 10⁹⁴(95-digit number)

19305619098568239461…64490783489473162239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.861 × 10⁹⁴(95-digit number)

38611238197136478923…28981566978946324479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.722 × 10⁹⁴(95-digit number)

77222476394272957847…57963133957892648959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.544 × 10⁹⁵(96-digit number)

15444495278854591569…15926267915785297919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.088 × 10⁹⁵(96-digit number)

30888990557709183139…31852535831570595839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.177 × 10⁹⁵(96-digit number)

61777981115418366278…63705071663141191679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.235 × 10⁹⁶(97-digit number)

12355596223083673255…27410143326282383359

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