Block #122,615

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/18/2013, 2:27:24 PM · Difficulty 9.7564 · 6,681,037 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

6f7575139206b6a7c2440d298cdc289e2345ba8a05e21f57e1e49a802c5cac04

View on Chainz ↗

Height

#122,615

Difficulty

9.756362

Transactions

Size

392 B

Version

Bits

09c1a0ef

Nonce

7,385

Timestamp

8/18/2013, 2:27:24 PM

Confirmations

6,681,037

Mined by

⛏️ P2SHAV4JSkBTdH6dgXwFcEGH5rGGFfdanJnZGt

Merkle Root

5648a16940e4ce33b63e5b98d6fadff2fb523b56b8785fc37d7f6e72ae5d9ca6

Transactions (2)

Coinbase794e9162f5d943…e58844d142db00

1 in → 1 out10.5000 XPM109 B

AV4JSkBT…danJnZGt

5e76fc85ee2652…0e233f4579ef02

1 in → 2 out10.5000 XPM191 B

AY8f8yN9…MYb79pci AXUtFnVB…2K4kmJnq

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.

1.564 × 10¹⁰⁰(101-digit number)

15648843459485517848…43692153171137062939

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

1.564 × 10¹⁰⁰(101-digit number)

15648843459485517848…43692153171137062939

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.129 × 10¹⁰⁰(101-digit number)

31297686918971035696…87384306342274125879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.259 × 10¹⁰⁰(101-digit number)

62595373837942071392…74768612684548251759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.251 × 10¹⁰¹(102-digit number)

12519074767588414278…49537225369096503519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.503 × 10¹⁰¹(102-digit number)

25038149535176828557…99074450738193007039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.007 × 10¹⁰¹(102-digit number)

50076299070353657114…98148901476386014079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.001 × 10¹⁰²(103-digit number)

10015259814070731422…96297802952772028159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.003 × 10¹⁰²(103-digit number)

20030519628141462845…92595605905544056319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.006 × 10¹⁰²(103-digit number)

40061039256282925691…85191211811088112639

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