Block #1,370,231

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/15/2015, 12:09:05 PM · Difficulty 10.8192 · 5,455,250 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dce3b802acc83610adb5ba7486c55b3dcf5fd15feb801ab074b93b516755893b

Height

#1,370,231

Difficulty

10.819156

Transactions

2

Size

596 B

Version

2

Bits

0ad1b434

Nonce

400,833,962

Timestamp

12/15/2015, 12:09:05 PM

Confirmations

5,455,250

Merkle Root

b819b8e73892591605206a55af49b67b57561537593a05c943c0d6ac4768e663
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.

4.168 × 10⁹⁷(98-digit number)
41680157757268157268…60651398237147791359
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
4.168 × 10⁹⁷(98-digit number)
41680157757268157268…60651398237147791359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
8.336 × 10⁹⁷(98-digit number)
83360315514536314537…21302796474295582719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.667 × 10⁹⁸(99-digit number)
16672063102907262907…42605592948591165439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.334 × 10⁹⁸(99-digit number)
33344126205814525814…85211185897182330879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.668 × 10⁹⁸(99-digit number)
66688252411629051629…70422371794364661759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.333 × 10⁹⁹(100-digit number)
13337650482325810325…40844743588729323519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.667 × 10⁹⁹(100-digit number)
26675300964651620651…81689487177458647039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.335 × 10⁹⁹(100-digit number)
53350601929303241303…63378974354917294079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.067 × 10¹⁰⁰(101-digit number)
10670120385860648260…26757948709834588159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.134 × 10¹⁰⁰(101-digit number)
21340240771721296521…53515897419669176319
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:57,847,942 XPM·at block #6,825,480 · 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