Block #112,127

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/11/2013, 7:54:54 PM · Difficulty 9.7175 · 6,683,300 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

a6e7b38650a2a4cd1d8a9bfb3e8c6f4b0bfc2274393944ee897e0494b543cfeb

View on Chainz ↗

Height

#112,127

Difficulty

9.717450

Transactions

Size

202 B

Version

Bits

09b7aad0

Nonce

295,569

Timestamp

8/11/2013, 7:54:54 PM

Confirmations

6,683,300

Mined by

⛏️ P2SHALLQzDjwYzXEhJsDvpwdS2bkdaZ3NcX8T9

Merkle Root

c1bee52eee9b57626d395b83f94a8bf35e86f40a703530f937e675894256c5a0

Transactions (1)

Coinbasec1bee52eee9b57…e675894256c5a0

1 in → 1 out10.5700 XPM109 B

ALLQzDjw…Z3NcX8T9

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.

4.875 × 10¹⁰¹(102-digit number)

48750307859807099558…15645644309429009389

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

4.875 × 10¹⁰¹(102-digit number)

48750307859807099558…15645644309429009389

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

9.750 × 10¹⁰¹(102-digit number)

97500615719614199117…31291288618858018779

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.950 × 10¹⁰²(103-digit number)

19500123143922839823…62582577237716037559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.900 × 10¹⁰²(103-digit number)

39000246287845679647…25165154475432075119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

7.800 × 10¹⁰²(103-digit number)

78000492575691359294…50330308950864150239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.560 × 10¹⁰³(104-digit number)

15600098515138271858…00660617901728300479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.120 × 10¹⁰³(104-digit number)

31200197030276543717…01321235803456600959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

6.240 × 10¹⁰³(104-digit number)

62400394060553087435…02642471606913201919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.248 × 10¹⁰⁴(105-digit number)

12480078812110617487…05284943213826403839

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