Block #508,806

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/24/2014, 3:28:10 PM · Difficulty 10.8190 · 6,285,554 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

e5abef80daea7c69e020c76e8c051751e5d4102723b2e8c71b994eedafb8eb95

View on Chainz ↗

Height

#508,806

Difficulty

10.818984

Transactions

Size

800 B

Version

Bits

0ad1a8ef

Nonce

5,245

Timestamp

4/24/2014, 3:28:10 PM

Confirmations

6,285,554

Merkle Root

3b7e80774f49740673657e6ba6b2253e1e34c3dcd988cf0bb25d024d0f5bff9c

Transactions (1)

Coinbase3b7e80774f4974…5d024d0f5bff9c

1 in → 19 out8.5300 XPM708 B

AQvZBsUo…hppgRZTJ AHwvxqCN…7z7foF67 ANNg88pG…ppn21sTe AdxPNkWD…ZMa9u34q 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.

1.345 × 10⁹⁹(100-digit number)

13455416616693075193…00765340455569602561

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

1.345 × 10⁹⁹(100-digit number)

13455416616693075193…00765340455569602561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.691 × 10⁹⁹(100-digit number)

26910833233386150387…01530680911139205121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.382 × 10⁹⁹(100-digit number)

53821666466772300775…03061361822278410241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.076 × 10¹⁰⁰(101-digit number)

10764333293354460155…06122723644556820481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.152 × 10¹⁰⁰(101-digit number)

21528666586708920310…12245447289113640961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.305 × 10¹⁰⁰(101-digit number)

43057333173417840620…24490894578227281921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

8.611 × 10¹⁰⁰(101-digit number)

86114666346835681240…48981789156454563841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.722 × 10¹⁰¹(102-digit number)

17222933269367136248…97963578312909127681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.444 × 10¹⁰¹(102-digit number)

34445866538734272496…95927156625818255361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

6.889 × 10¹⁰¹(102-digit number)

68891733077468544992…91854313251636510721

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