Block #911,226

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 1/26/2015, 10:36:36 PM · Difficulty 10.9316 · 5,932,075 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f93ea9073af6fa86f33c0865e8b167a1afc9d660295ebc8546f218e23b26b77f

Height

#911,226

Difficulty

10.931560

Transactions

3

Size

2.27 KB

Version

2

Bits

0aee7ab1

Nonce

212,766,252

Timestamp

1/26/2015, 10:36:36 PM

Confirmations

5,932,075

Merkle Root

8bb80318150c031c26914d5a8aacc6c60c07b7dac0a2cf0688e92b65e99e7034
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.

1.899 × 10⁹⁷(98-digit number)
18994689061596669949…34240248476055103999
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
1.899 × 10⁹⁷(98-digit number)
18994689061596669949…34240248476055103999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.798 × 10⁹⁷(98-digit number)
37989378123193339899…68480496952110207999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
7.597 × 10⁹⁷(98-digit number)
75978756246386679799…36960993904220415999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.519 × 10⁹⁸(99-digit number)
15195751249277335959…73921987808440831999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.039 × 10⁹⁸(99-digit number)
30391502498554671919…47843975616881663999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.078 × 10⁹⁸(99-digit number)
60783004997109343839…95687951233763327999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.215 × 10⁹⁹(100-digit number)
12156600999421868767…91375902467526655999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.431 × 10⁹⁹(100-digit number)
24313201998843737535…82751804935053311999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.862 × 10⁹⁹(100-digit number)
48626403997687475071…65503609870106623999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
9.725 × 10⁹⁹(100-digit number)
97252807995374950143…31007219740213247999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.945 × 10¹⁰⁰(101-digit number)
19450561599074990028…62014439480426495999
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,990,773 XPM·at block #6,843,300 · updates every 60s
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