Block #492,917

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/15/2014, 10:34:18 AM · Difficulty 10.6918 · 6,323,458 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e5aea02ca6ba5106f19e13b8cf168343d59992b54540497fc6beba232733a5ce

Height

#492,917

Difficulty

10.691762

Transactions

3

Size

708 B

Version

2

Bits

0ab11754

Nonce

204,725,308

Timestamp

4/15/2014, 10:34:18 AM

Confirmations

6,323,458

Merkle Root

efc254835fc234a79b8b5fb0acfe1b380ba691ea905245e3e3f1672b8a2fc777
Transactions (3)
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.

1.224 × 10⁹⁹(100-digit number)
12248072711220795640…64605373324767735039
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
1.224 × 10⁹⁹(100-digit number)
12248072711220795640…64605373324767735039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.449 × 10⁹⁹(100-digit number)
24496145422441591280…29210746649535470079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.899 × 10⁹⁹(100-digit number)
48992290844883182560…58421493299070940159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
9.798 × 10⁹⁹(100-digit number)
97984581689766365120…16842986598141880319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.959 × 10¹⁰⁰(101-digit number)
19596916337953273024…33685973196283760639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.919 × 10¹⁰⁰(101-digit number)
39193832675906546048…67371946392567521279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.838 × 10¹⁰⁰(101-digit number)
78387665351813092096…34743892785135042559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.567 × 10¹⁰¹(102-digit number)
15677533070362618419…69487785570270085119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.135 × 10¹⁰¹(102-digit number)
31355066140725236838…38975571140540170239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.271 × 10¹⁰¹(102-digit number)
62710132281450473677…77951142281080340479
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:57,775,128 XPM·at block #6,816,374 · 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.
Privacy Policy·

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