Block #130,694

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 8/23/2013, 6:25:39 PM · Difficulty 9.7858 · 6,686,087 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

dd04becfa5acb7a95eb1ecc170429a652852dce3262889aff6567aa82c9a2f85

View on Chainz ↗

Height

#130,694

Difficulty

9.785787

Transactions

Size

202 B

Version

Bits

09c92952

Nonce

29,418

Timestamp

8/23/2013, 6:25:39 PM

Confirmations

6,686,087

Mined by

⛏️ P2SHAcecj4WYP2kTRjXJMUTPed41WTwKtCNbS5

Merkle Root

850caeb7efbce3433e15912b1e864b66f7a95f41722ac854d6a6801c5468b375

Transactions (1)

Coinbase850caeb7efbce3…a6801c5468b375

1 in → 1 out10.4300 XPM109 B

Acecj4WY…wKtCNbS5

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.

9.927 × 10¹⁰¹(102-digit number)

99272928247865387015…09032185581086680929

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

9.927 × 10¹⁰¹(102-digit number)

99272928247865387015…09032185581086680929

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.985 × 10¹⁰²(103-digit number)

19854585649573077403…18064371162173361859

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.970 × 10¹⁰²(103-digit number)

39709171299146154806…36128742324346723719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.941 × 10¹⁰²(103-digit number)

79418342598292309612…72257484648693447439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.588 × 10¹⁰³(104-digit number)

15883668519658461922…44514969297386894879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.176 × 10¹⁰³(104-digit number)

31767337039316923845…89029938594773789759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.353 × 10¹⁰³(104-digit number)

63534674078633847690…78059877189547579519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.270 × 10¹⁰⁴(105-digit number)

12706934815726769538…56119754379095159039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.541 × 10¹⁰⁴(105-digit number)

25413869631453539076…12239508758190318079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.082 × 10¹⁰⁴(105-digit number)

50827739262907078152…24479017516380636159

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

Block #130,694

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