Block #1,253,935

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/26/2015, 3:13:27 AM · Difficulty 10.7926 · 5,540,920 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

45e313654d38fa5a8e66c566622d5f6d878fb3e0591d823b1b88f08b899390a0

View on Chainz ↗

Height

#1,253,935

Difficulty

10.792611

Transactions

Size

571 B

Version

Bits

0acae891

Nonce

436,669,467

Timestamp

9/26/2015, 3:13:27 AM

Confirmations

5,540,920

Mined by

⛏️ P2SHAQ6oyMrbpMFBf5BLCWSKyJEVojvhmDfayV

Merkle Root

9c1ff304e6de264f14e313cedba52120365bbc6748c8f2d676d5ab088a8e9ab1

Transactions (2)

Coinbasea42aa3066f172b…c1b9b69df32748

1 in → 1 out8.5800 XPM109 B

AQ6oyMrb…vhmDfayV

f63148f9f73421…329fa293d3aa5a

2 in → 2 out14.5121 XPM372 B

APaSkzEP…e9f176Qr AHwdNChB…iFNu4oDk

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.

3.029 × 10⁹⁴(95-digit number)

30292840543949892386…85781855126680816641

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

3.029 × 10⁹⁴(95-digit number)

30292840543949892386…85781855126680816641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.058 × 10⁹⁴(95-digit number)

60585681087899784773…71563710253361633281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.211 × 10⁹⁵(96-digit number)

12117136217579956954…43127420506723266561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.423 × 10⁹⁵(96-digit number)

24234272435159913909…86254841013446533121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.846 × 10⁹⁵(96-digit number)

48468544870319827818…72509682026893066241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.693 × 10⁹⁵(96-digit number)

96937089740639655637…45019364053786132481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.938 × 10⁹⁶(97-digit number)

19387417948127931127…90038728107572264961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.877 × 10⁹⁶(97-digit number)

38774835896255862254…80077456215144529921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.754 × 10⁹⁶(97-digit number)

77549671792511724509…60154912430289059841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.550 × 10⁹⁷(98-digit number)

15509934358502344901…20309824860578119681

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