Block #291,043

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/2/2013, 11:52:48 PM · Difficulty 9.9896 · 6,512,334 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

5458fe968829f14ff5bbe515bdb80b222b606ca4fa0c13e0bea120b49ac18fe8

View on Chainz ↗

Height

#291,043

Difficulty

9.989591

Transactions

Size

1.15 KB

Version

Bits

09fd55d3

Nonce

4,123

Timestamp

12/2/2013, 11:52:48 PM

Confirmations

6,512,334

Mined by

⛏️ paRe2AYcLTeXRXcXHePDnP5p1bevW8AbscgPops

Merkle Root

e0e97d7505da6d3db9661d2a8ac252f2f759c3cca14e94bd298731f753b22629

Transactions (1)

Coinbasee0e97d7505da6d…8731f753b22629

1 in → 30 out9.9900 XPM1.06 KB

AYcLTeXR…bscgPops AZninDSu…FvgDMwC4 Ad9pSzHt…cpJ3y2zz Acs9SHrk…QJSB8SFG AV6uuy6Z…MwQRdBX5

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.

4.686 × 10⁹⁸(99-digit number)

46860893986966761950…35045601446584960159

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

4.686 × 10⁹⁸(99-digit number)

46860893986966761950…35045601446584960159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

9.372 × 10⁹⁸(99-digit number)

93721787973933523901…70091202893169920319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.874 × 10⁹⁹(100-digit number)

18744357594786704780…40182405786339840639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.748 × 10⁹⁹(100-digit number)

37488715189573409560…80364811572679681279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

7.497 × 10⁹⁹(100-digit number)

74977430379146819121…60729623145359362559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.499 × 10¹⁰⁰(101-digit number)

14995486075829363824…21459246290718725119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.999 × 10¹⁰⁰(101-digit number)

29990972151658727648…42918492581437450239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.998 × 10¹⁰⁰(101-digit number)

59981944303317455296…85836985162874900479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.199 × 10¹⁰¹(102-digit number)

11996388860663491059…71673970325749800959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.399 × 10¹⁰¹(102-digit number)

23992777721326982118…43347940651499601919

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