Block #289,520

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/2/2013, 6:06:33 AM · Difficulty 9.9886 · 6,504,938 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

93b4d39c0faae735ef38369b857c7a44bca2963cd23d9c5793938efe9ba14054

View on Chainz ↗

Height

#289,520

Difficulty

9.988581

Transactions

Size

1.04 KB

Version

Bits

09fd13a8

Nonce

100,077

Timestamp

12/2/2013, 6:06:33 AM

Confirmations

6,504,938

Mined by

⛏️ jaR#l:AVKFC9nD3snNraYcHrou5F67vCJ9zTymTX

Merkle Root

df3d23a92bf1eeb5c70bd4dd7ec44c5849daaa14a0f36d64e8cab80517dfec13

Transactions (1)

Coinbasedf3d23a92bf1ee…cab80517dfec13

1 in → 27 out10.0100 XPM981 B

AVKFC9nD…J9zTymTX AZninDSu…FvgDMwC4 AdwTEXyC…NwbVbqZV AWXYBWKP…qQAoisBJ Ac5sZcdP…kzV4eckG

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.

2.258 × 10⁹⁰(91-digit number)

22586597491709037914…51970941769737906191

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

2.258 × 10⁹⁰(91-digit number)

22586597491709037914…51970941769737906191

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.517 × 10⁹⁰(91-digit number)

45173194983418075828…03941883539475812381

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.034 × 10⁹⁰(91-digit number)

90346389966836151656…07883767078951624761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.806 × 10⁹¹(92-digit number)

18069277993367230331…15767534157903249521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.613 × 10⁹¹(92-digit number)

36138555986734460662…31535068315806499041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.227 × 10⁹¹(92-digit number)

72277111973468921325…63070136631612998081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.445 × 10⁹²(93-digit number)

14455422394693784265…26140273263225996161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.891 × 10⁹²(93-digit number)

28910844789387568530…52280546526451992321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.782 × 10⁹²(93-digit number)

57821689578775137060…04561093052903984641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.156 × 10⁹³(94-digit number)

11564337915755027412…09122186105807969281

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