Block #1,349,367

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/1/2015, 3:56:51 AM · Difficulty 10.8104 · 5,453,332 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

e62e2f8d87a833f8e8736ff81d3d4d08e83641a7bba3d93dc457c3ef1e5a502c

View on Chainz ↗

Height

#1,349,367

Difficulty

10.810351

Transactions

Size

237 B

Version

Bits

0acf732f

Nonce

441,560

Timestamp

12/1/2015, 3:56:51 AM

Confirmations

5,453,332

Mined by

⛏️ P2SHAJCcxnuA2gFsc6HJAVptkiMzbSBeS8SCFB

Merkle Root

d56723441bac4d55869b4161dc333540e1fd7704a83eac03fad54487ee366b5c

Transactions (1)

Coinbased56723441bac4d…d54487ee366b5c

1 in → 2 out8.5400 XPM145 B

AJCcxnuA…BeS8SCFB Ac7DbgrK…XDMazkvn

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.

2.409 × 10⁹⁸(99-digit number)

24099445920027988289…31020305733165816001

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

2.409 × 10⁹⁸(99-digit number)

24099445920027988289…31020305733165816001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.819 × 10⁹⁸(99-digit number)

48198891840055976578…62040611466331632001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.639 × 10⁹⁸(99-digit number)

96397783680111953157…24081222932663264001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.927 × 10⁹⁹(100-digit number)

19279556736022390631…48162445865326528001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.855 × 10⁹⁹(100-digit number)

38559113472044781263…96324891730653056001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.711 × 10⁹⁹(100-digit number)

77118226944089562526…92649783461306112001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.542 × 10¹⁰⁰(101-digit number)

15423645388817912505…85299566922612224001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.084 × 10¹⁰⁰(101-digit number)

30847290777635825010…70599133845224448001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.169 × 10¹⁰⁰(101-digit number)

61694581555271650020…41198267690448896001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.233 × 10¹⁰¹(102-digit number)

12338916311054330004…82396535380897792001

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