Block #469,215

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/1/2014, 1:47:32 AM · Difficulty 10.4287 · 6,338,255 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f4fa46665b669f554b8503f50849f586d9e37d35b9f002151f6d501be0f97e98

Height

#469,215

Difficulty

10.428729

Transactions

5

Size

1.91 KB

Version

2

Bits

0a6dc127

Nonce

181,493

Timestamp

4/1/2014, 1:47:32 AM

Confirmations

6,338,255

Merkle Root

1c67c3c720046c23a4c13b5957b6082befdee794c61b350f2fb046b851daa68c
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.

9.506 × 10⁹⁶(97-digit number)
95065386856144055370…37182366638708126719
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
9.506 × 10⁹⁶(97-digit number)
95065386856144055370…37182366638708126719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.901 × 10⁹⁷(98-digit number)
19013077371228811074…74364733277416253439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.802 × 10⁹⁷(98-digit number)
38026154742457622148…48729466554832506879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.605 × 10⁹⁷(98-digit number)
76052309484915244296…97458933109665013759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.521 × 10⁹⁸(99-digit number)
15210461896983048859…94917866219330027519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.042 × 10⁹⁸(99-digit number)
30420923793966097718…89835732438660055039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.084 × 10⁹⁸(99-digit number)
60841847587932195437…79671464877320110079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.216 × 10⁹⁹(100-digit number)
12168369517586439087…59342929754640220159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.433 × 10⁹⁹(100-digit number)
24336739035172878174…18685859509280440319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.867 × 10⁹⁹(100-digit number)
48673478070345756349…37371719018560880639
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:57,703,785 XPM·at block #6,807,469 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

·Privacy Policy