Block #487,505

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/12/2014, 4:42:12 AM · Difficulty 10.6417 · 6,322,257 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d7e24457bb3c970671df43fe332a0b5479f4b827c69f6294adb3d657552f2cb8

Height

#487,505

Difficulty

10.641651

Transactions

1

Size

903 B

Version

2

Bits

0aa44339

Nonce

13,691

Timestamp

4/12/2014, 4:42:12 AM

Confirmations

6,322,257

Merkle Root

57eee7777ed8ec65724442fc8d5ff9be526d6edb275bbc31647f9f8cf0f598a4
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.

1.151 × 10¹⁰⁰(101-digit number)
11513872317280756280…81449981132271801199
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
1.151 × 10¹⁰⁰(101-digit number)
11513872317280756280…81449981132271801199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.302 × 10¹⁰⁰(101-digit number)
23027744634561512560…62899962264543602399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.605 × 10¹⁰⁰(101-digit number)
46055489269123025121…25799924529087204799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
9.211 × 10¹⁰⁰(101-digit number)
92110978538246050243…51599849058174409599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.842 × 10¹⁰¹(102-digit number)
18422195707649210048…03199698116348819199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.684 × 10¹⁰¹(102-digit number)
36844391415298420097…06399396232697638399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.368 × 10¹⁰¹(102-digit number)
73688782830596840194…12798792465395276799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.473 × 10¹⁰²(103-digit number)
14737756566119368038…25597584930790553599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.947 × 10¹⁰²(103-digit number)
29475513132238736077…51195169861581107199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
5.895 × 10¹⁰²(103-digit number)
58951026264477472155…02390339723162214399
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:57,722,183 XPM·at block #6,809,761 · 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