Block #1,363,644

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/10/2015, 9:06:40 AM · Difficulty 10.8452 · 5,449,308 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
952a69bcaeb9e5ddd137ee780e22cfec3d5f036d3b489e78171ef421b5375cd0

Height

#1,363,644

Difficulty

10.845232

Transactions

5

Size

1.38 KB

Version

2

Bits

0ad86128

Nonce

1,346,770,519

Timestamp

12/10/2015, 9:06:40 AM

Confirmations

5,449,308

Merkle Root

efd07bd85cb8e815e89050a146a01208a095f8515963095c6dff3f7f5903a5f8
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.

1.607 × 10⁹⁶(97-digit number)
16079418328274279869…67896204368222576639
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
1.607 × 10⁹⁶(97-digit number)
16079418328274279869…67896204368222576639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.215 × 10⁹⁶(97-digit number)
32158836656548559738…35792408736445153279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.431 × 10⁹⁶(97-digit number)
64317673313097119477…71584817472890306559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.286 × 10⁹⁷(98-digit number)
12863534662619423895…43169634945780613119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.572 × 10⁹⁷(98-digit number)
25727069325238847791…86339269891561226239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.145 × 10⁹⁷(98-digit number)
51454138650477695582…72678539783122452479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.029 × 10⁹⁸(99-digit number)
10290827730095539116…45357079566244904959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.058 × 10⁹⁸(99-digit number)
20581655460191078232…90714159132489809919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.116 × 10⁹⁸(99-digit number)
41163310920382156465…81428318264979619839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
8.232 × 10⁹⁸(99-digit number)
82326621840764312931…62856636529959239679
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:57,747,656 XPM·at block #6,812,951 · updates every 60s
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