Block #683,657

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 8/19/2014, 7:08:21 AM · Difficulty 10.9589 · 6,134,375 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

6d9a63bb40315a5430ac288315c2be647c753a17eb7634ef5accaa084729bb09

View on Chainz ↗

Height

#683,657

Difficulty

10.958880

Transactions

Size

243 B

Version

Bits

0af57923

Nonce

138,504,635

Timestamp

8/19/2014, 7:08:21 AM

Confirmations

6,134,375

Mined by

⛏️ P2SHATrzKxLEMcqj8iissCT2aSSgyrdnfypiwk

Merkle Root

98853924455884598e73f0eef5bd0a7983d4917a16e55dd0e985fbfb5b49da8d

Transactions (1)

Coinbase98853924455884…85fbfb5b49da8d

1 in → 2 out8.3100 XPM152 B

ATrzKxLE…dnfypiwk ALPu3s2c…EJXLjVFh

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.

6.390 × 10⁹⁷(98-digit number)

63902776640918121372…97936930277902850559

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

6.390 × 10⁹⁷(98-digit number)

63902776640918121372…97936930277902850559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.278 × 10⁹⁸(99-digit number)

12780555328183624274…95873860555805701119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.556 × 10⁹⁸(99-digit number)

25561110656367248549…91747721111611402239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.112 × 10⁹⁸(99-digit number)

51122221312734497098…83495442223222804479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.022 × 10⁹⁹(100-digit number)

10224444262546899419…66990884446445608959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.044 × 10⁹⁹(100-digit number)

20448888525093798839…33981768892891217919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.089 × 10⁹⁹(100-digit number)

40897777050187597678…67963537785782435839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.179 × 10⁹⁹(100-digit number)

81795554100375195356…35927075571564871679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.635 × 10¹⁰⁰(101-digit number)

16359110820075039071…71854151143129743359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.271 × 10¹⁰⁰(101-digit number)

32718221640150078142…43708302286259486719

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 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

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 1CC formula:

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

Cross-reference on Chainz Explorer

Block #683,657

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