Block #3,370,795

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 9/27/2019, 12:26:51 AM · Difficulty 10.9950 · 3,435,123 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f11c36bbf8de8f3f9d219d72aba833fb937e800c57d257a078c634149084f618

Height

#3,370,795

Difficulty

10.994974

Transactions

4

Size

1.81 KB

Version

2

Bits

0afeb696

Nonce

1,089,914,272

Timestamp

9/27/2019, 12:26:51 AM

Confirmations

3,435,123

Merkle Root

df919dbe03945361b05d08335cf1cb899eec8ccb477a457d5ae8ea159ba9c2c1
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.

5.184 × 10⁹⁵(96-digit number)
51847329880009801942…63390227494558667081
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
5.184 × 10⁹⁵(96-digit number)
51847329880009801942…63390227494558667081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.036 × 10⁹⁶(97-digit number)
10369465976001960388…26780454989117334161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.073 × 10⁹⁶(97-digit number)
20738931952003920776…53560909978234668321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.147 × 10⁹⁶(97-digit number)
41477863904007841553…07121819956469336641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.295 × 10⁹⁶(97-digit number)
82955727808015683107…14243639912938673281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.659 × 10⁹⁷(98-digit number)
16591145561603136621…28487279825877346561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.318 × 10⁹⁷(98-digit number)
33182291123206273243…56974559651754693121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.636 × 10⁹⁷(98-digit number)
66364582246412546486…13949119303509386241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.327 × 10⁹⁸(99-digit number)
13272916449282509297…27898238607018772481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.654 × 10⁹⁸(99-digit number)
26545832898565018594…55796477214037544961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
5.309 × 10⁹⁸(99-digit number)
53091665797130037189…11592954428075089921
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:57,691,421 XPM·at block #6,805,917 · updates every 60s
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