Block #1,487,808

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/7/2016, 6:18:07 PM · Difficulty 10.7190 · 5,346,066 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d3b7590499c038afaef3b27b0d176dedc9e8579e37b2bc801fa17e944def1d00

Height

#1,487,808

Difficulty

10.719032

Transactions

2

Size

1.86 KB

Version

2

Bits

0ab81275

Nonce

330,022,457

Timestamp

3/7/2016, 6:18:07 PM

Confirmations

5,346,066

Merkle Root

965bb2d888c73fb2ccf1cf1ce59b2881daf796c6f42b914bc6ded09d7a8d117c
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.

1.129 × 10⁹⁶(97-digit number)
11290595220427671436…20735000111593618561
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
1.129 × 10⁹⁶(97-digit number)
11290595220427671436…20735000111593618561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.258 × 10⁹⁶(97-digit number)
22581190440855342873…41470000223187237121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.516 × 10⁹⁶(97-digit number)
45162380881710685746…82940000446374474241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.032 × 10⁹⁶(97-digit number)
90324761763421371492…65880000892748948481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.806 × 10⁹⁷(98-digit number)
18064952352684274298…31760001785497896961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.612 × 10⁹⁷(98-digit number)
36129904705368548596…63520003570995793921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.225 × 10⁹⁷(98-digit number)
72259809410737097193…27040007141991587841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.445 × 10⁹⁸(99-digit number)
14451961882147419438…54080014283983175681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.890 × 10⁹⁸(99-digit number)
28903923764294838877…08160028567966351361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.780 × 10⁹⁸(99-digit number)
57807847528589677755…16320057135932702721
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:57,915,224 XPM·at block #6,833,873 · updates every 60s
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