Block #237,401

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/1/2013, 12:52:00 AM · Difficulty 9.9496 · 6,575,287 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
905e4ebb8ab36e0a91cc4531542f1d13c7ef5e1efc5c089691508a2b60a1fc39

Height

#237,401

Difficulty

9.949589

Transactions

2

Size

723 B

Version

2

Bits

09f31842

Nonce

51,830

Timestamp

11/1/2013, 12:52:00 AM

Confirmations

6,575,287

Merkle Root

cc0583fc08938c4bc6cf646efa3deabe5ab81173985a73ab1b9e9096e4fc876a
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.

1.113 × 10⁹⁷(98-digit number)
11135543534457448652…35768380360751142399
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
1.113 × 10⁹⁷(98-digit number)
11135543534457448652…35768380360751142399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.227 × 10⁹⁷(98-digit number)
22271087068914897305…71536760721502284799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.454 × 10⁹⁷(98-digit number)
44542174137829794611…43073521443004569599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
8.908 × 10⁹⁷(98-digit number)
89084348275659589222…86147042886009139199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.781 × 10⁹⁸(99-digit number)
17816869655131917844…72294085772018278399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.563 × 10⁹⁸(99-digit number)
35633739310263835688…44588171544036556799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.126 × 10⁹⁸(99-digit number)
71267478620527671377…89176343088073113599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.425 × 10⁹⁹(100-digit number)
14253495724105534275…78352686176146227199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.850 × 10⁹⁹(100-digit number)
28506991448211068551…56705372352292454399
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,745,539 XPM·at block #6,812,687 · 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