Block #2,150,360

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/7/2017, 4:22:18 PM · Difficulty 10.8990 · 4,659,705 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8ae3b9668fdde4e60a7728945d2248d4a9ef7a587f420af40652d4d53127044e

Height

#2,150,360

Difficulty

10.899021

Transactions

2

Size

3.45 KB

Version

2

Bits

0ae6263c

Nonce

1,896,066,674

Timestamp

6/7/2017, 4:22:18 PM

Confirmations

4,659,705

Merkle Root

bdda719c79ff7e6489715b2e898955c97d650514481ea053367572869da907e5
Transactions (2)
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.

4.234 × 10⁹²(93-digit number)
42343484524751448289…84360076667982712819
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
4.234 × 10⁹²(93-digit number)
42343484524751448289…84360076667982712819
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
8.468 × 10⁹²(93-digit number)
84686969049502896579…68720153335965425639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.693 × 10⁹³(94-digit number)
16937393809900579315…37440306671930851279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.387 × 10⁹³(94-digit number)
33874787619801158631…74880613343861702559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.774 × 10⁹³(94-digit number)
67749575239602317263…49761226687723405119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.354 × 10⁹⁴(95-digit number)
13549915047920463452…99522453375446810239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.709 × 10⁹⁴(95-digit number)
27099830095840926905…99044906750893620479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.419 × 10⁹⁴(95-digit number)
54199660191681853810…98089813501787240959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.083 × 10⁹⁵(96-digit number)
10839932038336370762…96179627003574481919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.167 × 10⁹⁵(96-digit number)
21679864076672741524…92359254007148963839
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:57,724,591 XPM·at block #6,810,064 · 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