Block #1,452,812

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/12/2016, 7:03:26 AM · Difficulty 10.7309 · 5,356,950 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
198441592eee78ff07552cfe0c8c75fbb6c93a84e6542322cc40fbb939b807b7

Height

#1,452,812

Difficulty

10.730907

Transactions

3

Size

10.59 KB

Version

2

Bits

0abb1cb6

Nonce

940,563,273

Timestamp

2/12/2016, 7:03:26 AM

Confirmations

5,356,950

Merkle Root

bbb6d7edabdfae89f4e09e06f12d1377036a9a40448ae53aad4659585d88f160
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.

6.691 × 10⁹²(93-digit number)
66917672205457263967…28488240229475507921
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
6.691 × 10⁹²(93-digit number)
66917672205457263967…28488240229475507921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.338 × 10⁹³(94-digit number)
13383534441091452793…56976480458951015841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.676 × 10⁹³(94-digit number)
26767068882182905586…13952960917902031681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.353 × 10⁹³(94-digit number)
53534137764365811173…27905921835804063361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.070 × 10⁹⁴(95-digit number)
10706827552873162234…55811843671608126721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.141 × 10⁹⁴(95-digit number)
21413655105746324469…11623687343216253441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.282 × 10⁹⁴(95-digit number)
42827310211492648938…23247374686432506881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.565 × 10⁹⁴(95-digit number)
85654620422985297877…46494749372865013761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.713 × 10⁹⁵(96-digit number)
17130924084597059575…92989498745730027521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.426 × 10⁹⁵(96-digit number)
34261848169194119151…85978997491460055041
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:57,722,183 XPM·at block #6,809,761 · updates every 60s
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