Block #138,953

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/28/2013, 5:20:03 PM · Difficulty 9.8289 · 6,652,936 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

de850566d9f0abe7c79df1bee82ea4821f34018c0fe2b766bb1067107725ea36

View on Chainz ↗

Height

#138,953

Difficulty

9.828889

Transactions

Size

198 B

Version

Bits

09d4320f

Nonce

13,331

Timestamp

8/28/2013, 5:20:03 PM

Confirmations

6,652,936

Merkle Root

f3af488a89c3034b60bcb42af7530f5a736bf4383f2191b94fd2727d6714093b

Transactions (1)

Coinbasef3af488a89c303…d2727d6714093b

1 in → 1 out10.3400 XPM109 B

Ac8C5CfD…SojGXosx

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.

2.612 × 10⁹³(94-digit number)

26128871923678467270…29638580950107763199

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

2.612 × 10⁹³(94-digit number)

26128871923678467270…29638580950107763199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.225 × 10⁹³(94-digit number)

52257743847356934540…59277161900215526399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.045 × 10⁹⁴(95-digit number)

10451548769471386908…18554323800431052799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.090 × 10⁹⁴(95-digit number)

20903097538942773816…37108647600862105599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.180 × 10⁹⁴(95-digit number)

41806195077885547632…74217295201724211199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.361 × 10⁹⁴(95-digit number)

83612390155771095264…48434590403448422399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.672 × 10⁹⁵(96-digit number)

16722478031154219052…96869180806896844799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.344 × 10⁹⁵(96-digit number)

33444956062308438105…93738361613793689599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.688 × 10⁹⁵(96-digit number)

66889912124616876211…87476723227587379199

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