Block #384,805

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/1/2014, 9:02:08 AM · Difficulty 10.4018 · 6,431,809 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bcebba0174e654a530be05fe6e7b23ccac2e70a779fff8fd1f2ddc51197779db

Height

#384,805

Difficulty

10.401834

Transactions

4

Size

890 B

Version

2

Bits

0a66de99

Nonce

11,246

Timestamp

2/1/2014, 9:02:08 AM

Confirmations

6,431,809

Merkle Root

da0c2eac9d7dc9bd6cd2015ed1bb52cd5c1e105efacc2a36d586f4de4bc314fb
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.

2.255 × 10¹⁰⁵(106-digit number)
22557885540766411337…30491902033408486401
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
2.255 × 10¹⁰⁵(106-digit number)
22557885540766411337…30491902033408486401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.511 × 10¹⁰⁵(106-digit number)
45115771081532822675…60983804066816972801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.023 × 10¹⁰⁵(106-digit number)
90231542163065645350…21967608133633945601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.804 × 10¹⁰⁶(107-digit number)
18046308432613129070…43935216267267891201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.609 × 10¹⁰⁶(107-digit number)
36092616865226258140…87870432534535782401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.218 × 10¹⁰⁶(107-digit number)
72185233730452516280…75740865069071564801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.443 × 10¹⁰⁷(108-digit number)
14437046746090503256…51481730138143129601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.887 × 10¹⁰⁷(108-digit number)
28874093492181006512…02963460276286259201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.774 × 10¹⁰⁷(108-digit number)
57748186984362013024…05926920552572518401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.154 × 10¹⁰⁸(109-digit number)
11549637396872402604…11853841105145036801
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:57,777,034 XPM·at block #6,816,613 · updates every 60s
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