Block #507,439

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/23/2014, 5:57:19 PM · Difficulty 10.8162 · 6,288,834 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

60e0add0de0e7e84e9dd4747423b0c7de1da42cec07798a821fd9b108f8857f0

View on Chainz ↗

Height

#507,439

Difficulty

10.816225

Transactions

Size

833 B

Version

Bits

0ad0f41b

Nonce

110,497

Timestamp

4/23/2014, 5:57:19 PM

Confirmations

6,288,834

Mined by

⛏️ aSWAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

1be28966b7d1b74d07a898f2bf8ab66f62f43523592ba2802cccf42cc363ca33

Transactions (1)

Coinbase1be28966b7d1b7…ccf42cc363ca33

1 in → 20 out8.5300 XPM743 B

AQvZBsUo…hppgRZTJ AHwvxqCN…7z7foF67 ANNg88pG…ppn21sTe AUbecsVa…i8zo8qRf ATKK7iFz…wZm46KN1

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.

7.037 × 10⁹⁵(96-digit number)

70378161888972600454…92415193349930152161

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

7.037 × 10⁹⁵(96-digit number)

70378161888972600454…92415193349930152161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.407 × 10⁹⁶(97-digit number)

14075632377794520090…84830386699860304321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.815 × 10⁹⁶(97-digit number)

28151264755589040181…69660773399720608641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

5.630 × 10⁹⁶(97-digit number)

56302529511178080363…39321546799441217281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.126 × 10⁹⁷(98-digit number)

11260505902235616072…78643093598882434561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.252 × 10⁹⁷(98-digit number)

22521011804471232145…57286187197764869121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.504 × 10⁹⁷(98-digit number)

45042023608942464291…14572374395529738241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

9.008 × 10⁹⁷(98-digit number)

90084047217884928582…29144748791059476481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.801 × 10⁹⁸(99-digit number)

18016809443576985716…58289497582118952961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.603 × 10⁹⁸(99-digit number)

36033618887153971432…16578995164237905921

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