Block #1,240,453

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 9/17/2015, 7:56:45 AM · Difficulty 10.7563 · 5,567,475 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cdae44312c65aa0b63d2548ed2239ddfc9b7ca1517b665828c1ca5dcc0ac4c5b

Height

#1,240,453

Difficulty

10.756280

Transactions

2

Size

427 B

Version

2

Bits

0ac19b8b

Nonce

1,423,861,269

Timestamp

9/17/2015, 7:56:45 AM

Confirmations

5,567,475

Merkle Root

cace6a5016417790af8c4dbd668ee9a260ee0265eb1aa85611e77501d707f9b2
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.

2.629 × 10⁹⁷(98-digit number)
26296508456846802443…38545626756097802239
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
2.629 × 10⁹⁷(98-digit number)
26296508456846802443…38545626756097802239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.259 × 10⁹⁷(98-digit number)
52593016913693604887…77091253512195604479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.051 × 10⁹⁸(99-digit number)
10518603382738720977…54182507024391208959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.103 × 10⁹⁸(99-digit number)
21037206765477441955…08365014048782417919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.207 × 10⁹⁸(99-digit number)
42074413530954883910…16730028097564835839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
8.414 × 10⁹⁸(99-digit number)
84148827061909767820…33460056195129671679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.682 × 10⁹⁹(100-digit number)
16829765412381953564…66920112390259343359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.365 × 10⁹⁹(100-digit number)
33659530824763907128…33840224780518686719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.731 × 10⁹⁹(100-digit number)
67319061649527814256…67680449561037373439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.346 × 10¹⁰⁰(101-digit number)
13463812329905562851…35360899122074746879
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:57,707,461 XPM·at block #6,807,927 · 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