Block #1,462,713

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/18/2016, 10:04:07 AM · Difficulty 10.7831 · 5,378,366 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
29fe29c6242a786a60139cf56599e17eeca843872057f4b2f805e358aaa34d4e

Height

#1,462,713

Difficulty

10.783084

Transactions

3

Size

2.51 KB

Version

2

Bits

0ac8782a

Nonce

1,018,191,183

Timestamp

2/18/2016, 10:04:07 AM

Confirmations

5,378,366

Merkle Root

3abf48c7bcda717533b82877756fc5635c03a9f90705494fbb6a2cb43cdf3308
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.

7.007 × 10⁹²(93-digit number)
70073234629344431416…80088990432323978879
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
7.007 × 10⁹²(93-digit number)
70073234629344431416…80088990432323978879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.401 × 10⁹³(94-digit number)
14014646925868886283…60177980864647957759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.802 × 10⁹³(94-digit number)
28029293851737772566…20355961729295915519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.605 × 10⁹³(94-digit number)
56058587703475545133…40711923458591831039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.121 × 10⁹⁴(95-digit number)
11211717540695109026…81423846917183662079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.242 × 10⁹⁴(95-digit number)
22423435081390218053…62847693834367324159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.484 × 10⁹⁴(95-digit number)
44846870162780436106…25695387668734648319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
8.969 × 10⁹⁴(95-digit number)
89693740325560872213…51390775337469296639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.793 × 10⁹⁵(96-digit number)
17938748065112174442…02781550674938593279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.587 × 10⁹⁵(96-digit number)
35877496130224348885…05563101349877186559
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:57,972,995 XPM·at block #6,841,078 · 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