Block #200,941

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/9/2013, 8:02:47 AM · Difficulty 9.8907 · 6,607,960 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d81e169c81291dc47d5ac4021790c5c9db690741d13ea76cf2276eb796314952

Height

#200,941

Difficulty

9.890665

Transactions

5

Size

6.15 KB

Version

2

Bits

09e40297

Nonce

1,277

Timestamp

10/9/2013, 8:02:47 AM

Confirmations

6,607,960

Merkle Root

5ccb774182e01265014da8b9d638f27069f9581b346cedea4361af8e71b517fb
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.

3.502 × 10⁹⁸(99-digit number)
35020188010550513162…19220366320793740199
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
3.502 × 10⁹⁸(99-digit number)
35020188010550513162…19220366320793740199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.004 × 10⁹⁸(99-digit number)
70040376021101026325…38440732641587480399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.400 × 10⁹⁹(100-digit number)
14008075204220205265…76881465283174960799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.801 × 10⁹⁹(100-digit number)
28016150408440410530…53762930566349921599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.603 × 10⁹⁹(100-digit number)
56032300816880821060…07525861132699843199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.120 × 10¹⁰⁰(101-digit number)
11206460163376164212…15051722265399686399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.241 × 10¹⁰⁰(101-digit number)
22412920326752328424…30103444530799372799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.482 × 10¹⁰⁰(101-digit number)
44825840653504656848…60206889061598745599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
8.965 × 10¹⁰⁰(101-digit number)
89651681307009313696…20413778123197491199
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:57,715,261 XPM·at block #6,808,900 · updates every 60s
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