Block #2,015,460

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/9/2017, 1:47:12 PM · Difficulty 10.7088 · 4,821,503 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
698242c44126cd9483e6f6e21e6bf4760bd578386f18e8df6c743fec42d9977d

Height

#2,015,460

Difficulty

10.708841

Transactions

2

Size

1019 B

Version

2

Bits

0ab5769e

Nonce

100,506,173

Timestamp

3/9/2017, 1:47:12 PM

Confirmations

4,821,503

Merkle Root

fc94c680599d6db0c20669c6f582e0616a811a58054017684ed4bcdb9f5d0463
Transactions (2)
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.

8.038 × 10⁹⁵(96-digit number)
80386901343469566659…22877250850794931201
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
8.038 × 10⁹⁵(96-digit number)
80386901343469566659…22877250850794931201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.607 × 10⁹⁶(97-digit number)
16077380268693913331…45754501701589862401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.215 × 10⁹⁶(97-digit number)
32154760537387826663…91509003403179724801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.430 × 10⁹⁶(97-digit number)
64309521074775653327…83018006806359449601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.286 × 10⁹⁷(98-digit number)
12861904214955130665…66036013612718899201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.572 × 10⁹⁷(98-digit number)
25723808429910261330…32072027225437798401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.144 × 10⁹⁷(98-digit number)
51447616859820522661…64144054450875596801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.028 × 10⁹⁸(99-digit number)
10289523371964104532…28288108901751193601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.057 × 10⁹⁸(99-digit number)
20579046743928209064…56576217803502387201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.115 × 10⁹⁸(99-digit number)
41158093487856418129…13152435607004774401
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:57,940,003 XPM·at block #6,836,962 · updates every 60s
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