Block #126,154

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/20/2013, 5:02:47 PM · Difficulty 9.7797 · 6,676,972 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

32e4f7368ff83264dca22af5e1f234ba5a6c1de78358da7c91838342f2cda8bb

View on Chainz ↗

Height

#126,154

Difficulty

9.779742

Transactions

Size

201 B

Version

Bits

09c79d25

Nonce

475,795

Timestamp

8/20/2013, 5:02:47 PM

Confirmations

6,676,972

Mined by

⛏️ P2SHAbB3aifuT9ri2zqZMbJ723U3z6wrbJL6FT

Merkle Root

e72c290784d78da37b1368884668fd2f5f607b344c629925ed33d45360fce811

Transactions (1)

Coinbasee72c290784d78d…33d45360fce811

1 in → 1 out10.4400 XPM109 B

AbB3aifu…wrbJL6FT

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.

8.200 × 10⁹⁹(100-digit number)

82004302118656040650…54935773198618311709

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

8.200 × 10⁹⁹(100-digit number)

82004302118656040650…54935773198618311709

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.640 × 10¹⁰⁰(101-digit number)

16400860423731208130…09871546397236623419

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.280 × 10¹⁰⁰(101-digit number)

32801720847462416260…19743092794473246839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.560 × 10¹⁰⁰(101-digit number)

65603441694924832520…39486185588946493679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.312 × 10¹⁰¹(102-digit number)

13120688338984966504…78972371177892987359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.624 × 10¹⁰¹(102-digit number)

26241376677969933008…57944742355785974719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.248 × 10¹⁰¹(102-digit number)

52482753355939866016…15889484711571949439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.049 × 10¹⁰²(103-digit number)

10496550671187973203…31778969423143898879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.099 × 10¹⁰²(103-digit number)

20993101342375946406…63557938846287797759

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