Block #2,283,576

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 9/5/2017, 2:00:03 PM · Difficulty 10.9554 · 4,547,308 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d939d801b3badc6c7ca6d82dd082da845402340d4145cc7f5bdafec7016202d1

Height

#2,283,576

Difficulty

10.955377

Transactions

3

Size

652 B

Version

2

Bits

0af4939a

Nonce

297,324,036

Timestamp

9/5/2017, 2:00:03 PM

Confirmations

4,547,308

Merkle Root

b6d9591bb5203a93ce326961939335378504c73373f55b185aa8e95f5cd28a91
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.

1.274 × 10⁹⁷(98-digit number)
12743819142224161126…44722595059236840961
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
1.274 × 10⁹⁷(98-digit number)
12743819142224161126…44722595059236840961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.548 × 10⁹⁷(98-digit number)
25487638284448322252…89445190118473681921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.097 × 10⁹⁷(98-digit number)
50975276568896644504…78890380236947363841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.019 × 10⁹⁸(99-digit number)
10195055313779328900…57780760473894727681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.039 × 10⁹⁸(99-digit number)
20390110627558657801…15561520947789455361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.078 × 10⁹⁸(99-digit number)
40780221255117315603…31123041895578910721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.156 × 10⁹⁸(99-digit number)
81560442510234631206…62246083791157821441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.631 × 10⁹⁹(100-digit number)
16312088502046926241…24492167582315642881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.262 × 10⁹⁹(100-digit number)
32624177004093852482…48984335164631285761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.524 × 10⁹⁹(100-digit number)
65248354008187704965…97968670329262571521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.304 × 10¹⁰⁰(101-digit number)
13049670801637540993…95937340658525143041
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:57,891,208 XPM·at block #6,830,883 · updates every 60s
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