Block #507,796

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/23/2014, 11:21:27 PM · Difficulty 10.8174 · 6,285,229 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

b26570a5afea29f3b2d64570e68b9612b3c1c58085f974195f75e95a05ed9e69

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Height

#507,796

Difficulty

10.817385

Transactions

Size

834 B

Version

Bits

0ad14028

Nonce

1,124,013,983

Timestamp

4/23/2014, 11:21:27 PM

Confirmations

6,285,229

Merkle Root

502b2382035654fad3c0d4822be71f127cc094fce3796d8b2d019c7117d09054

Transactions (1)

Coinbase502b2382035654…019c7117d09054

1 in → 20 out8.5300 XPM742 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.

1.441 × 10⁹⁹(100-digit number)

14417216065730398965…15920741809434634241

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

1.441 × 10⁹⁹(100-digit number)

14417216065730398965…15920741809434634241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.883 × 10⁹⁹(100-digit number)

28834432131460797931…31841483618869268481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.766 × 10⁹⁹(100-digit number)

57668864262921595862…63682967237738536961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.153 × 10¹⁰⁰(101-digit number)

11533772852584319172…27365934475477073921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.306 × 10¹⁰⁰(101-digit number)

23067545705168638345…54731868950954147841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.613 × 10¹⁰⁰(101-digit number)

46135091410337276690…09463737901908295681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.227 × 10¹⁰⁰(101-digit number)

92270182820674553380…18927475803816591361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.845 × 10¹⁰¹(102-digit number)

18454036564134910676…37854951607633182721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.690 × 10¹⁰¹(102-digit number)

36908073128269821352…75709903215266365441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

7.381 × 10¹⁰¹(102-digit number)

73816146256539642704…51419806430532730881

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