Block #1,115,218

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 6/18/2015, 8:22:11 AM · Difficulty 10.9192 · 5,711,789 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
aef611e662d077dfa74fda350c9dd6323cfb62f0dbc0f475a2a0808bde99a593

Height

#1,115,218

Difficulty

10.919178

Transactions

2

Size

5.77 KB

Version

2

Bits

0aeb4f3b

Nonce

943,207,468

Timestamp

6/18/2015, 8:22:11 AM

Confirmations

5,711,789

Merkle Root

a944b953564fabdb11f21f97fbf21862116010c976cf158deeb8d65702592449
Transactions (2)
1 in → 1 out8.4600 XPM116 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.

1.458 × 10⁹⁸(99-digit number)
14586790122376641978…39651549556635279359
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
1.458 × 10⁹⁸(99-digit number)
14586790122376641978…39651549556635279359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.917 × 10⁹⁸(99-digit number)
29173580244753283957…79303099113270558719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.834 × 10⁹⁸(99-digit number)
58347160489506567914…58606198226541117439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.166 × 10⁹⁹(100-digit number)
11669432097901313582…17212396453082234879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.333 × 10⁹⁹(100-digit number)
23338864195802627165…34424792906164469759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.667 × 10⁹⁹(100-digit number)
46677728391605254331…68849585812328939519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
9.335 × 10⁹⁹(100-digit number)
93355456783210508662…37699171624657879039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.867 × 10¹⁰⁰(101-digit number)
18671091356642101732…75398343249315758079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.734 × 10¹⁰⁰(101-digit number)
37342182713284203465…50796686498631516159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.468 × 10¹⁰⁰(101-digit number)
74684365426568406930…01593372997263032319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.493 × 10¹⁰¹(102-digit number)
14936873085313681386…03186745994526064639
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:57,860,232 XPM·at block #6,827,006 · updates every 60s
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