Block #202,219

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/10/2013, 2:17:28 AM · Difficulty 9.8946 · 6,603,471 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fab0a9608585033880ffd6cb8a73d8f60bd1d40aff7e5ca082881c953e26ade3

Height

#202,219

Difficulty

9.894636

Transactions

2

Size

389 B

Version

2

Bits

09e506e4

Nonce

8,607

Timestamp

10/10/2013, 2:17:28 AM

Confirmations

6,603,471

Merkle Root

6b6996ddce6cfa1b7d12094912a7d2a73f7f76008200f5faae19748d1197aa10
Transactions (2)
1 in → 1 out10.2100 XPM109 B
1 in → 1 out199.9900 XPM192 B
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.

7.736 × 10⁹⁰(91-digit number)
77367057548253868291…52082359612045366999
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
7.736 × 10⁹⁰(91-digit number)
77367057548253868291…52082359612045366999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.547 × 10⁹¹(92-digit number)
15473411509650773658…04164719224090733999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.094 × 10⁹¹(92-digit number)
30946823019301547316…08329438448181467999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.189 × 10⁹¹(92-digit number)
61893646038603094633…16658876896362935999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.237 × 10⁹²(93-digit number)
12378729207720618926…33317753792725871999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.475 × 10⁹²(93-digit number)
24757458415441237853…66635507585451743999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.951 × 10⁹²(93-digit number)
49514916830882475706…33271015170903487999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
9.902 × 10⁹²(93-digit number)
99029833661764951413…66542030341806975999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.980 × 10⁹³(94-digit number)
19805966732352990282…33084060683613951999
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:57,689,602 XPM·at block #6,805,689 · updates every 60s
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