Block #1,323,844

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/12/2015, 3:10:14 PM · Difficulty 10.8486 · 5,492,232 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
edc3564d1af1f0d98a0f9d5701555599020fd60ff363271ac65bfd73b1de118d

Height

#1,323,844

Difficulty

10.848559

Transactions

2

Size

2.04 KB

Version

2

Bits

0ad93b26

Nonce

38,565,147

Timestamp

11/12/2015, 3:10:14 PM

Confirmations

5,492,232

Merkle Root

315989c59c5d2ad92e8fb166c2d71ede535fcabbaa6be3506f7bc6410ace8b9f
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.

4.149 × 10⁹⁶(97-digit number)
41490700442902912683…72244380261862942719
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
4.149 × 10⁹⁶(97-digit number)
41490700442902912683…72244380261862942719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
8.298 × 10⁹⁶(97-digit number)
82981400885805825366…44488760523725885439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.659 × 10⁹⁷(98-digit number)
16596280177161165073…88977521047451770879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.319 × 10⁹⁷(98-digit number)
33192560354322330146…77955042094903541759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.638 × 10⁹⁷(98-digit number)
66385120708644660293…55910084189807083519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.327 × 10⁹⁸(99-digit number)
13277024141728932058…11820168379614167039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.655 × 10⁹⁸(99-digit number)
26554048283457864117…23640336759228334079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.310 × 10⁹⁸(99-digit number)
53108096566915728234…47280673518456668159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.062 × 10⁹⁹(100-digit number)
10621619313383145646…94561347036913336319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.124 × 10⁹⁹(100-digit number)
21243238626766291293…89122694073826672639
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,772,726 XPM·at block #6,816,075 · updates every 60s
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