Block #1,168,200

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/24/2015, 10:57:20 AM · Difficulty 10.9353 · 5,658,666 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e188ce55da78bab0f48bdf41ef632f355c1d784f6b19f0024d66e6f4680906a8

Height

#1,168,200

Difficulty

10.935273

Transactions

3

Size

3.38 KB

Version

2

Bits

0aef6e0d

Nonce

1,502,876,327

Timestamp

7/24/2015, 10:57:20 AM

Confirmations

5,658,666

Merkle Root

93b8c0b7dbbe335553b524f0fb31bf80422aa8b9025590e442f24832bacaa69f
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.

2.299 × 10⁹⁶(97-digit number)
22992024431355819362…40932808628785269761
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
2.299 × 10⁹⁶(97-digit number)
22992024431355819362…40932808628785269761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.598 × 10⁹⁶(97-digit number)
45984048862711638725…81865617257570539521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.196 × 10⁹⁶(97-digit number)
91968097725423277450…63731234515141079041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.839 × 10⁹⁷(98-digit number)
18393619545084655490…27462469030282158081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.678 × 10⁹⁷(98-digit number)
36787239090169310980…54924938060564316161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.357 × 10⁹⁷(98-digit number)
73574478180338621960…09849876121128632321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.471 × 10⁹⁸(99-digit number)
14714895636067724392…19699752242257264641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.942 × 10⁹⁸(99-digit number)
29429791272135448784…39399504484514529281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.885 × 10⁹⁸(99-digit number)
58859582544270897568…78799008969029058561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.177 × 10⁹⁹(100-digit number)
11771916508854179513…57598017938058117121
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,859,090 XPM·at block #6,826,865 · updates every 60s
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