Block #1,521,501

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/1/2016, 12:04:18 PM · Difficulty 10.5893 · 5,309,976 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
01f2f1a9965c1c6bd7570b2a718a16d64761de83fe926debeb46186de83f6022

Height

#1,521,501

Difficulty

10.589286

Transactions

2

Size

1.31 KB

Version

2

Bits

0a96db6d

Nonce

1,037,796,153

Timestamp

4/1/2016, 12:04:18 PM

Confirmations

5,309,976

Merkle Root

36afb99d04d7c7d8192900bec3154733010c456bd58b527af2e8b5f371574fae
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.

1.491 × 10⁹²(93-digit number)
14912654749399112449…94258506551784171251
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
1.491 × 10⁹²(93-digit number)
14912654749399112449…94258506551784171251
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.982 × 10⁹²(93-digit number)
29825309498798224899…88517013103568342501
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.965 × 10⁹²(93-digit number)
59650618997596449798…77034026207136685001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.193 × 10⁹³(94-digit number)
11930123799519289959…54068052414273370001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.386 × 10⁹³(94-digit number)
23860247599038579919…08136104828546740001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.772 × 10⁹³(94-digit number)
47720495198077159838…16272209657093480001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.544 × 10⁹³(94-digit number)
95440990396154319677…32544419314186960001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.908 × 10⁹⁴(95-digit number)
19088198079230863935…65088838628373920001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.817 × 10⁹⁴(95-digit number)
38176396158461727870…30177677256747840001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.635 × 10⁹⁴(95-digit number)
76352792316923455741…60355354513495680001
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:57,895,908 XPM·at block #6,831,476 · updates every 60s
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