Block #128,318

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/22/2013, 3:44:16 AM · Difficulty 9.7834 · 6,675,708 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

5d1237691a92709e044400168029ff567b99058acc5a171d9053e94e340870dd

View on Chainz ↗

Height

#128,318

Difficulty

9.783428

Transactions

Size

552 B

Version

Bits

09c88eb5

Nonce

186,731

Timestamp

8/22/2013, 3:44:16 AM

Confirmations

6,675,708

Mined by

⛏️ P2SHAbB3aifuT9ri2zqZMbJ723U3z6wrbJL6FT

Merkle Root

06a08eb9f220bd5cb5c211316b688b41b7094323c342eee01696eaf65eabeacb

Transactions (3)

Coinbase0caa6ffbe50a31…d6bd50da2715b5

1 in → 1 out10.4500 XPM109 B

AbB3aifu…wrbJL6FT

836e51026120c1…b1533970c70f48

1 in → 2 out10.5300 XPM192 B

AQXnPCd8…H13K1uw2 AZJKmqth…xqSDzny2

7cd203400b7f74…44b4094cf81d7f

1 in → 1 out10.4400 XPM159 B

AXGg13jX…xq9Bq7T1

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.

1.064 × 10¹⁰⁰(101-digit number)

10644001376790799659…27128650549385503961

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

1.064 × 10¹⁰⁰(101-digit number)

10644001376790799659…27128650549385503961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.128 × 10¹⁰⁰(101-digit number)

21288002753581599318…54257301098771007921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.257 × 10¹⁰⁰(101-digit number)

42576005507163198636…08514602197542015841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

8.515 × 10¹⁰⁰(101-digit number)

85152011014326397272…17029204395084031681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.703 × 10¹⁰¹(102-digit number)

17030402202865279454…34058408790168063361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.406 × 10¹⁰¹(102-digit number)

34060804405730558909…68116817580336126721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.812 × 10¹⁰¹(102-digit number)

68121608811461117818…36233635160672253441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.362 × 10¹⁰²(103-digit number)

13624321762292223563…72467270321344506881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.724 × 10¹⁰²(103-digit number)

27248643524584447127…44934540642689013761

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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer