Block #228,614

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/26/2013, 3:22:19 PM · Difficulty 9.9379 · 6,570,749 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bd7fa1721ad88de637aebc54c62c9401bc59f47b5f807dfc3f38e9f419aef9be

Height

#228,614

Difficulty

9.937935

Transactions

1

Size

936 B

Version

2

Bits

09f01c87

Nonce

58,117

Timestamp

10/26/2013, 3:22:19 PM

Confirmations

6,570,749

Merkle Root

63cf0e852fa4b8b5d0d0cb0eafb43bb5851fff0947ee040aff39b36cee968363
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.

3.162 × 10⁹⁸(99-digit number)
31628428817706880059…66406994301642007039
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.

1
origin − 1
3.162 × 10⁹⁸(99-digit number)
31628428817706880059…66406994301642007039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.325 × 10⁹⁸(99-digit number)
63256857635413760118…32813988603284014079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.265 × 10⁹⁹(100-digit number)
12651371527082752023…65627977206568028159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.530 × 10⁹⁹(100-digit number)
25302743054165504047…31255954413136056319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.060 × 10⁹⁹(100-digit number)
50605486108331008094…62511908826272112639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.012 × 10¹⁰⁰(101-digit number)
10121097221666201618…25023817652544225279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.024 × 10¹⁰⁰(101-digit number)
20242194443332403237…50047635305088450559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.048 × 10¹⁰⁰(101-digit number)
40484388886664806475…00095270610176901119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
8.096 × 10¹⁰⁰(101-digit number)
80968777773329612951…00190541220353802239
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, …
Circulating Supply:57,638,951 XPM·at block #6,799,362 · updates every 60s
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