Block #79,398

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/23/2013, 11:07:06 AM · Difficulty 9.2452 · 6,724,349 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

be92a68ef753aa495e368c921b02c71696eab74271446380a6eae8d4c4df0ff5

View on Chainz ↗

Height

#79,398

Difficulty

9.245174

Transactions

Size

591 B

Version

Bits

093ec3b7

Nonce

198

Timestamp

7/23/2013, 11:07:06 AM

Confirmations

6,724,349

Mined by

⛏️ P2SHAHGi8wDB5Q1pnktV2RKKJj33qeeKomrPdd

Merkle Root

2b0e9680bd14c5bfaabab44eceae75eb0afa9aa9a9f2b60df82e8b22ac7f85a1

Transactions (2)

Coinbase4ff90ff0f3a54c…a133ba96c4530c

1 in → 1 out11.6900 XPM110 B

AHGi8wDB…eKomrPdd

f95a327ceda92b…a6d4ae06b63235

3 in → 1 out37.1000 XPM388 B

AWXmemfk…KQwTkea7

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.

1.599 × 10¹⁰¹(102-digit number)

15991211200293886379…77626619768164993271

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

1.599 × 10¹⁰¹(102-digit number)

15991211200293886379…77626619768164993271

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.198 × 10¹⁰¹(102-digit number)

31982422400587772759…55253239536329986541

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.396 × 10¹⁰¹(102-digit number)

63964844801175545518…10506479072659973081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.279 × 10¹⁰²(103-digit number)

12792968960235109103…21012958145319946161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.558 × 10¹⁰²(103-digit number)

25585937920470218207…42025916290639892321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.117 × 10¹⁰²(103-digit number)

51171875840940436414…84051832581279784641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.023 × 10¹⁰³(104-digit number)

10234375168188087282…68103665162559569281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.046 × 10¹⁰³(104-digit number)

20468750336376174565…36207330325119138561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.093 × 10¹⁰³(104-digit number)

40937500672752349131…72414660650238277121

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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