Block #2,468,108

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/11/2018, 2:01:17 PM · Difficulty 10.9603 · 4,371,064 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ae953907c710c50125d26666b5176143321028e7dec29fb6e83f485a455740fc

Height

#2,468,108

Difficulty

10.960279

Transactions

8

Size

3.33 KB

Version

2

Bits

0af5d4d9

Nonce

241,868,059

Timestamp

1/11/2018, 2:01:17 PM

Confirmations

4,371,064

Merkle Root

2381d8e08016d077d1dfaca96c3e145409d24fec3ceeefa485cbc0faad90fc28
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.

2.811 × 10⁹⁴(95-digit number)
28115586516001647399…07961901016489603201
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
2.811 × 10⁹⁴(95-digit number)
28115586516001647399…07961901016489603201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.623 × 10⁹⁴(95-digit number)
56231173032003294799…15923802032979206401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.124 × 10⁹⁵(96-digit number)
11246234606400658959…31847604065958412801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.249 × 10⁹⁵(96-digit number)
22492469212801317919…63695208131916825601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.498 × 10⁹⁵(96-digit number)
44984938425602635839…27390416263833651201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
8.996 × 10⁹⁵(96-digit number)
89969876851205271679…54780832527667302401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.799 × 10⁹⁶(97-digit number)
17993975370241054335…09561665055334604801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.598 × 10⁹⁶(97-digit number)
35987950740482108671…19123330110669209601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.197 × 10⁹⁶(97-digit number)
71975901480964217343…38246660221338419201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.439 × 10⁹⁷(98-digit number)
14395180296192843468…76493320442676838401
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:57,957,657 XPM·at block #6,839,171 · updates every 60s
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