Block #140,922

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/29/2013, 11:29:29 PM · Difficulty 9.8343 · 6,651,657 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

3e365298742495cb03f7579a178505622f6b693510ae16268f028debb280e4f3

View on Chainz ↗

Height

#140,922

Difficulty

9.834290

Transactions

Size

196 B

Version

Bits

09d59401

Nonce

78,838

Timestamp

8/29/2013, 11:29:29 PM

Confirmations

6,651,657

Merkle Root

97a7addd5847a192a2d5e8c34a53a21f1b0538794b49e78edacca139785e6199

Transactions (1)

Coinbase97a7addd5847a1…cca139785e6199

1 in → 1 out10.3200 XPM109 B

AKhaGKFX…KjeAXtBv

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.

5.876 × 10⁸⁸(89-digit number)

58765581648822011409…58009682797789400159

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

5.876 × 10⁸⁸(89-digit number)

58765581648822011409…58009682797789400159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.175 × 10⁸⁹(90-digit number)

11753116329764402281…16019365595578800319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.350 × 10⁸⁹(90-digit number)

23506232659528804563…32038731191157600639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.701 × 10⁸⁹(90-digit number)

47012465319057609127…64077462382315201279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

9.402 × 10⁸⁹(90-digit number)

94024930638115218255…28154924764630402559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.880 × 10⁹⁰(91-digit number)

18804986127623043651…56309849529260805119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.760 × 10⁹⁰(91-digit number)

37609972255246087302…12619699058521610239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.521 × 10⁹⁰(91-digit number)

75219944510492174604…25239398117043220479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.504 × 10⁹¹(92-digit number)

15043988902098434920…50478796234086440959

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