Block #192,726

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/4/2013, 1:45:53 AM · Difficulty 9.8747 · 6,602,998 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

0eafb388b24fedfeb89df322ec9de741ab6648b0d4679e9a84a6512b17bb7fc4

View on Chainz ↗

Height

#192,726

Difficulty

9.874723

Transactions

Size

3.70 KB

Version

Bits

09dfede0

Nonce

1,164,750,166

Timestamp

10/4/2013, 1:45:53 AM

Confirmations

6,602,998

Mined by

⛏️ RNHAKoHGbXLom1M8Gju1g5wQuz5nGAMALbdsK

Merkle Root

0417c1b9e3395236476d6a6de1a135aded73c7f3a0135aa5c5fe15804698c120

Transactions (1)

Coinbase0417c1b9e33952…fe15804698c120

1 in → 107 out10.2000 XPM3.61 KB

AKoHGbXL…AMALbdsK APtCCTjk…etXBZujq AZUh3Jk2…PRHDo2Aj AVW3nNAF…ihzUUPP1 AZ1SeNMM…6tkj61SE

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.

2.509 × 10⁹⁴(95-digit number)

25099305998926131311…91497169230735308001

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

2.509 × 10⁹⁴(95-digit number)

25099305998926131311…91497169230735308001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.019 × 10⁹⁴(95-digit number)

50198611997852262623…82994338461470616001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.003 × 10⁹⁵(96-digit number)

10039722399570452524…65988676922941232001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.007 × 10⁹⁵(96-digit number)

20079444799140905049…31977353845882464001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.015 × 10⁹⁵(96-digit number)

40158889598281810098…63954707691764928001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

8.031 × 10⁹⁵(96-digit number)

80317779196563620197…27909415383529856001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.606 × 10⁹⁶(97-digit number)

16063555839312724039…55818830767059712001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.212 × 10⁹⁶(97-digit number)

32127111678625448078…11637661534119424001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.425 × 10⁹⁶(97-digit number)

64254223357250896157…23275323068238848001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.285 × 10⁹⁷(98-digit number)

12850844671450179231…46550646136477696001

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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer