Block #1,519,696

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/31/2016, 5:29:09 AM · Difficulty 10.5915 · 5,277,168 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

e11eede24c534923b41b2657a600022642876fe6f93b296501145879714c3993

View on Chainz ↗

Height

#1,519,696

Difficulty

10.591538

Transactions

Size

237 B

Version

Bits

0a976f04

Nonce

21,824

Timestamp

3/31/2016, 5:29:09 AM

Confirmations

5,277,168

Mined by

⛏️ P2SHAJCcxnuA2gFsc6HJAVptkiMzbSBeS8SCFB

Merkle Root

54f7215c5382c216e9c85c60ddba7d9930873b50cad6c944b2f7ee7028f422db

Transactions (1)

Coinbase54f7215c5382c2…f7ee7028f422db

1 in → 2 out8.9000 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.

7.673 × 10⁹⁸(99-digit number)

76735426428155626587…52833746046028525701

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

7.673 × 10⁹⁸(99-digit number)

76735426428155626587…52833746046028525701

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.534 × 10⁹⁹(100-digit number)

15347085285631125317…05667492092057051401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.069 × 10⁹⁹(100-digit number)

30694170571262250635…11334984184114102801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.138 × 10⁹⁹(100-digit number)

61388341142524501270…22669968368228205601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.227 × 10¹⁰⁰(101-digit number)

12277668228504900254…45339936736456411201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.455 × 10¹⁰⁰(101-digit number)

24555336457009800508…90679873472912822401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.911 × 10¹⁰⁰(101-digit number)

49110672914019601016…81359746945825644801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

9.822 × 10¹⁰⁰(101-digit number)

98221345828039202032…62719493891651289601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.964 × 10¹⁰¹(102-digit number)

19644269165607840406…25438987783302579201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.928 × 10¹⁰¹(102-digit number)

39288538331215680813…50877975566605158401

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