Block #2,887,228

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 10/19/2018, 3:15:34 AM · Difficulty 11.6209 · 3,957,398 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ccb4df5c767fbc3773f6a294a72ff3ffee3a5786d385d9a84e69f1c7f75cf3ff

Height

#2,887,228

Difficulty

11.620879

Transactions

8

Size

2.12 KB

Version

2

Bits

0b9ef1e7

Nonce

444,532,899

Timestamp

10/19/2018, 3:15:34 AM

Confirmations

3,957,398

Merkle Root

e753fbcf1f3d14d0ef9d86ae9ae9b93dacd2ddeedd1fe9029198a7d301d0c4d0
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.

4.689 × 10⁹⁴(95-digit number)
46899879705484341255…76090393627003699201
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
4.689 × 10⁹⁴(95-digit number)
46899879705484341255…76090393627003699201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
9.379 × 10⁹⁴(95-digit number)
93799759410968682511…52180787254007398401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.875 × 10⁹⁵(96-digit number)
18759951882193736502…04361574508014796801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.751 × 10⁹⁵(96-digit number)
37519903764387473004…08723149016029593601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
7.503 × 10⁹⁵(96-digit number)
75039807528774946009…17446298032059187201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.500 × 10⁹⁶(97-digit number)
15007961505754989201…34892596064118374401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.001 × 10⁹⁶(97-digit number)
30015923011509978403…69785192128236748801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.003 × 10⁹⁶(97-digit number)
60031846023019956807…39570384256473497601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.200 × 10⁹⁷(98-digit number)
12006369204603991361…79140768512946995201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.401 × 10⁹⁷(98-digit number)
24012738409207982722…58281537025893990401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
4.802 × 10⁹⁷(98-digit number)
48025476818415965445…16563074051787980801
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:58,001,413 XPM·at block #6,844,625 · updates every 60s
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