Block #284,862

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/30/2013, 7:04:32 AM · Difficulty 9.9834 · 6,519,936 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

ac56f7b159d9f58d3288ee7f2a1ce7b326ef66f53de4e9b3a75551558a598c14

View on Chainz ↗

Height

#284,862

Difficulty

9.983424

Transactions

Size

1.21 KB

Version

Bits

09fbc1a9

Nonce

103,705

Timestamp

11/30/2013, 7:04:32 AM

Confirmations

6,519,936

Mined by

⛏️ XaRAKEwr54iEsuosjdBu66r2F564f9BfmMkRh

Merkle Root

439040f2f5ae668b8285c6cbcb63cbadb25425e3f25762e7f204ed1efec1f014

Transactions (1)

Coinbase439040f2f5ae66…04ed1efec1f014

1 in → 32 out10.0000 XPM1.12 KB

AKEwr54i…9BfmMkRh Ac5sZcdP…kzV4eckG Acs9SHrk…QJSB8SFG ANo4YY1x…vnsPRDSU ASdFbQ41…WNAgRmiJ

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.

4.516 × 10⁹⁴(95-digit number)

45169156925357256747…55188457254137655319

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

4.516 × 10⁹⁴(95-digit number)

45169156925357256747…55188457254137655319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

9.033 × 10⁹⁴(95-digit number)

90338313850714513495…10376914508275310639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.806 × 10⁹⁵(96-digit number)

18067662770142902699…20753829016550621279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.613 × 10⁹⁵(96-digit number)

36135325540285805398…41507658033101242559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

7.227 × 10⁹⁵(96-digit number)

72270651080571610796…83015316066202485119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.445 × 10⁹⁶(97-digit number)

14454130216114322159…66030632132404970239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.890 × 10⁹⁶(97-digit number)

28908260432228644318…32061264264809940479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.781 × 10⁹⁶(97-digit number)

57816520864457288637…64122528529619880959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.156 × 10⁹⁷(98-digit number)

11563304172891457727…28245057059239761919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.312 × 10⁹⁷(98-digit number)

23126608345782915454…56490114118479523839

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