Block #208,811

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 10/14/2013, 5:46:21 AM · Difficulty 9.9073 · 6,596,366 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0a0487814ee9af9c86e619a20e05538714e23f842f1f08394f716f224d79afaa

Height

#208,811

Difficulty

9.907276

Transactions

3

Size

944 B

Version

2

Bits

09e84342

Nonce

116,387

Timestamp

10/14/2013, 5:46:21 AM

Confirmations

6,596,366

Merkle Root

5fd18b14176c782da588697834046a78435b23f6afea9a99978ae6941ac66624
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.

1.298 × 10⁹¹(92-digit number)
12989083676993602926…07322508900935700479
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
1.298 × 10⁹¹(92-digit number)
12989083676993602926…07322508900935700479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.597 × 10⁹¹(92-digit number)
25978167353987205852…14645017801871400959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.195 × 10⁹¹(92-digit number)
51956334707974411704…29290035603742801919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.039 × 10⁹²(93-digit number)
10391266941594882340…58580071207485603839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.078 × 10⁹²(93-digit number)
20782533883189764681…17160142414971207679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.156 × 10⁹²(93-digit number)
41565067766379529363…34320284829942415359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
8.313 × 10⁹²(93-digit number)
83130135532759058726…68640569659884830719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.662 × 10⁹³(94-digit number)
16626027106551811745…37281139319769661439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.325 × 10⁹³(94-digit number)
33252054213103623490…74562278639539322879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.650 × 10⁹³(94-digit number)
66504108426207246981…49124557279078645759
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,685,485 XPM·at block #6,805,176 · updates every 60s
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