Block #212,168

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/16/2013, 3:15:25 AM · Difficulty 9.9183 · 6,580,239 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

2eaa4bb6161fa791acd14dfae4afcf120e0141564f0adb6234cdfba343331e11

View on Chainz ↗

Height

#212,168

Difficulty

9.918300

Transactions

Size

1.45 KB

Version

Bits

09eb15b9

Nonce

52,772

Timestamp

10/16/2013, 3:15:25 AM

Confirmations

6,580,239

Merkle Root

8f1ed02c00a0675ef62405d2671e519686615cfecaf5ec1388c96def558003c3

Transactions (4)

Coinbaseeeaeed5208ec4e…1c15281a0fa025

1 in → 1 out10.1800 XPM109 B

Adri1peA…DAdav5HF

b21cf4f6e32ca6…777e8c8ed74570

3 in → 2 out31.4700 XPM420 B

AFz9fXym…wh4UqpkL AZPYv9J4…v9tZ5FXg

dfde0deb107d41…99c7b02ff58927

2 in → 2 out10.7016 XPM374 B

APuv56Q9…D7VL7uEN AHyHEeYQ…XuELsExj

277bc3bb972542…ef03b2e7f9fd5a

3 in → 2 out11.0700 XPM488 B

AewsRHmQ…AuQygCzV AFz9fXym…wh4UqpkL

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.

1.132 × 10⁹³(94-digit number)

11325620591053797445…41588982236607185599

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

1.132 × 10⁹³(94-digit number)

11325620591053797445…41588982236607185599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.265 × 10⁹³(94-digit number)

22651241182107594891…83177964473214371199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.530 × 10⁹³(94-digit number)

45302482364215189783…66355928946428742399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.060 × 10⁹³(94-digit number)

90604964728430379567…32711857892857484799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.812 × 10⁹⁴(95-digit number)

18120992945686075913…65423715785714969599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.624 × 10⁹⁴(95-digit number)

36241985891372151827…30847431571429939199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.248 × 10⁹⁴(95-digit number)

72483971782744303654…61694863142859878399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.449 × 10⁹⁵(96-digit number)

14496794356548860730…23389726285719756799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.899 × 10⁹⁵(96-digit number)

28993588713097721461…46779452571439513599

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