Block #1,145,466

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 7/8/2015, 8:38:48 PM · Difficulty 10.9308 · 5,697,560 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8234b870315c4da624d62c89658abe1480bae2f741a78bf7ccd40bc0776891c4

Height

#1,145,466

Difficulty

10.930805

Transactions

3

Size

30.57 KB

Version

2

Bits

0aee4938

Nonce

1,108,222,933

Timestamp

7/8/2015, 8:38:48 PM

Confirmations

5,697,560

Merkle Root

f3ef4330b6f9c33150e592acf2de34c33ec3c596856fa0272046ebf0eb802e44
Transactions (3)
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.

5.342 × 10⁹²(93-digit number)
53425366505908100466…29001244448340467361
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
5.342 × 10⁹²(93-digit number)
53425366505908100466…29001244448340467361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.068 × 10⁹³(94-digit number)
10685073301181620093…58002488896680934721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.137 × 10⁹³(94-digit number)
21370146602363240186…16004977793361869441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.274 × 10⁹³(94-digit number)
42740293204726480373…32009955586723738881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.548 × 10⁹³(94-digit number)
85480586409452960746…64019911173447477761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.709 × 10⁹⁴(95-digit number)
17096117281890592149…28039822346894955521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.419 × 10⁹⁴(95-digit number)
34192234563781184298…56079644693789911041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.838 × 10⁹⁴(95-digit number)
68384469127562368597…12159289387579822081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.367 × 10⁹⁵(96-digit number)
13676893825512473719…24318578775159644161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.735 × 10⁹⁵(96-digit number)
27353787651024947439…48637157550319288321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
5.470 × 10⁹⁵(96-digit number)
54707575302049894878…97274315100638576641
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,988,562 XPM·at block #6,843,025 · updates every 60s
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