Block #82,845

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/25/2013, 5:21:58 PM · Difficulty 9.2736 · 6,712,710 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

3ac4a3c7a052192d09b4f640d786932f08feab6f0f9ce4db5545fc34bf905016

View on Chainz ↗

Height

#82,845

Difficulty

9.273585

Transactions

Size

397 B

Version

Bits

094609ae

Nonce

7,551

Timestamp

7/25/2013, 5:21:58 PM

Confirmations

6,712,710

Mined by

⛏️ P2SHAHGi8wDB5Q1pnktV2RKKJj33qeeKomrPdd

Merkle Root

fe3da3bfe3ccf9d5ad43cd40dc923fa705066482e1821e31362d9389d696a01c

Transactions (2)

Coinbase094a8217926b28…22c0a01ad2e2b1

1 in → 1 out11.6200 XPM109 B

AHGi8wDB…eKomrPdd

8b6b2a370febf8…0957e90c220afc

1 in → 2 out15.6800 XPM192 B

ATBKWbYT…LWfJG89g Aawn9XBp…AT8dv9Uf

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.

9.804 × 10¹⁰⁹(110-digit number)

98043408372291365803…95065992087346953919

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

9.804 × 10¹⁰⁹(110-digit number)

98043408372291365803…95065992087346953919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.960 × 10¹¹⁰(111-digit number)

19608681674458273160…90131984174693907839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.921 × 10¹¹⁰(111-digit number)

39217363348916546321…80263968349387815679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.843 × 10¹¹⁰(111-digit number)

78434726697833092642…60527936698775631359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.568 × 10¹¹¹(112-digit number)

15686945339566618528…21055873397551262719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.137 × 10¹¹¹(112-digit number)

31373890679133237057…42111746795102525439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.274 × 10¹¹¹(112-digit number)

62747781358266474114…84223493590205050879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.254 × 10¹¹²(113-digit number)

12549556271653294822…68446987180410101759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.509 × 10¹¹²(113-digit number)

25099112543306589645…36893974360820203519

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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer