Block #2,386,744

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/20/2017, 12:10:35 AM · Difficulty 10.8737 · 4,456,676 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a15f83df9776376f0a1c7b4371a70f5d5f32440c6b90415cc740f7f8dacb6e82

Height

#2,386,744

Difficulty

10.873739

Transactions

2

Size

461 B

Version

2

Bits

0adfad5f

Nonce

1,543,909,502

Timestamp

11/20/2017, 12:10:35 AM

Confirmations

4,456,676

Merkle Root

0287becaab75f11781590b2154f1bc87f4a04f62b737260985f5b9a8ae6e2aa2
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.

2.767 × 10⁹⁶(97-digit number)
27676872627769610047…66460635611001969921
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
2.767 × 10⁹⁶(97-digit number)
27676872627769610047…66460635611001969921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.535 × 10⁹⁶(97-digit number)
55353745255539220095…32921271222003939841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.107 × 10⁹⁷(98-digit number)
11070749051107844019…65842542444007879681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.214 × 10⁹⁷(98-digit number)
22141498102215688038…31685084888015759361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.428 × 10⁹⁷(98-digit number)
44282996204431376076…63370169776031518721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
8.856 × 10⁹⁷(98-digit number)
88565992408862752152…26740339552063037441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.771 × 10⁹⁸(99-digit number)
17713198481772550430…53480679104126074881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.542 × 10⁹⁸(99-digit number)
35426396963545100860…06961358208252149761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.085 × 10⁹⁸(99-digit number)
70852793927090201721…13922716416504299521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.417 × 10⁹⁹(100-digit number)
14170558785418040344…27845432833008599041
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:57,991,728 XPM·at block #6,843,419 · updates every 60s
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