Block #1,137,566

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 7/2/2015, 11:25:19 PM · Difficulty 10.9380 · 5,686,932 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f6500a6f78b3f09254f70f48fa4a775186733f8ef690945dcce0f61f8087e6b9

Height

#1,137,566

Difficulty

10.938004

Transactions

2

Size

2.05 KB

Version

2

Bits

0af02109

Nonce

538,378,957

Timestamp

7/2/2015, 11:25:19 PM

Confirmations

5,686,932

Merkle Root

d26e7e445f59a802222d9bf47016ad011bae627068429aa37576502961cb4d31
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.

1.895 × 10⁹⁷(98-digit number)
18953890299699524748…23874812084463692799
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
1.895 × 10⁹⁷(98-digit number)
18953890299699524748…23874812084463692799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.790 × 10⁹⁷(98-digit number)
37907780599399049497…47749624168927385599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
7.581 × 10⁹⁷(98-digit number)
75815561198798098995…95499248337854771199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.516 × 10⁹⁸(99-digit number)
15163112239759619799…90998496675709542399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.032 × 10⁹⁸(99-digit number)
30326224479519239598…81996993351419084799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.065 × 10⁹⁸(99-digit number)
60652448959038479196…63993986702838169599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.213 × 10⁹⁹(100-digit number)
12130489791807695839…27987973405676339199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.426 × 10⁹⁹(100-digit number)
24260979583615391678…55975946811352678399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.852 × 10⁹⁹(100-digit number)
48521959167230783357…11951893622705356799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
9.704 × 10⁹⁹(100-digit number)
97043918334461566714…23903787245410713599
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:57,840,057 XPM·at block #6,824,497 · 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