Block #193,983

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/4/2013, 8:38:16 PM · Difficulty 9.8780 · 6,613,177 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

a102d35c92ea246881651a72556fd6691d872747bd75be816470b295094d3423

View on Chainz ↗

Height

#193,983

Difficulty

9.878029

Transactions

Size

3.53 KB

Version

Bits

09e0c680

Nonce

1,164,974,179

Timestamp

10/4/2013, 8:38:16 PM

Confirmations

6,613,177

Mined by

⛏️ RO&Ab8mfHU7wK1M7AaMuC3Q1gfu8Y38SseZM1

Merkle Root

5c02fd0879e716aa861fd9a22347da571ccfad58b652cbfd2ba0d8e53d85ed1f

Transactions (1)

Coinbase5c02fd0879e716…a0d8e53d85ed1f

1 in → 102 out10.1900 XPM3.45 KB

Ab8mfHU7…38SseZM1 AcfrRTbM…yqBXdeSV AXjaQhW5…TW8rjDYX AWJHU8CF…JUjqyNaX AeLXg8qu…77XGoqwh

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.

4.150 × 10⁸⁹(90-digit number)

41505989397923491932…49176482762552383999

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

4.150 × 10⁸⁹(90-digit number)

41505989397923491932…49176482762552383999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

8.301 × 10⁸⁹(90-digit number)

83011978795846983865…98352965525104767999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.660 × 10⁹⁰(91-digit number)

16602395759169396773…96705931050209535999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.320 × 10⁹⁰(91-digit number)

33204791518338793546…93411862100419071999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.640 × 10⁹⁰(91-digit number)

66409583036677587092…86823724200838143999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.328 × 10⁹¹(92-digit number)

13281916607335517418…73647448401676287999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.656 × 10⁹¹(92-digit number)

26563833214671034836…47294896803352575999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.312 × 10⁹¹(92-digit number)

53127666429342069673…94589793606705151999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.062 × 10⁹²(93-digit number)

10625533285868413934…89179587213410303999

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

Block #193,983

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