XPM Prime Explorer symbol
XPMPrime Explorer

Block #194,643

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/5/2013, 6:16:14 AM Β· Difficulty 9.8802 Β· 6,632,114 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ce91a9e787d779125631c2b44aa54b216c2650d278425a854f3064a722e901b8
View on Chainz β†—

Height

#194,643

Difficulty

9.880152

Transactions

1

Size

198 B

Version

2

Bits

09e151a8

Nonce

97,413

Timestamp

10/5/2013, 6:16:14 AM

Confirmations

6,632,114

Mined by

⛏️ P2SHAbGZZ5j9xYn1T2NM8sUHpoY2ocPsAgN9dv

Merkle Root

affab7a6ce8a9a293954028ce5736ccda360a800b4d7f63e62ce7983e4a25562
Transactions (1)
Coinbaseaffab7a6ce8a9a…ce7983e4a25562
1 in β†’ 1 out10.2300 XPM109 B
AbGZZ5j9…PsAgN9dv
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.273 Γ— 10⁹²(93-digit number)
22735867816912300512…23897870397342979999
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.273 Γ— 10⁹²(93-digit number)
22735867816912300512…23897870397342979999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.547 Γ— 10⁹²(93-digit number)
45471735633824601024…47795740794685959999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.094 Γ— 10⁹²(93-digit number)
90943471267649202049…95591481589371919999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.818 Γ— 10⁹³(94-digit number)
18188694253529840409…91182963178743839999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.637 Γ— 10⁹³(94-digit number)
36377388507059680819…82365926357487679999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.275 Γ— 10⁹³(94-digit number)
72754777014119361639…64731852714975359999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.455 Γ— 10⁹⁴(95-digit number)
14550955402823872327…29463705429950719999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.910 Γ— 10⁹⁴(95-digit number)
29101910805647744655…58927410859901439999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.820 Γ— 10⁹⁴(95-digit number)
58203821611295489311…17854821719802879999
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,858,214 XPMΒ·at block #6,826,756 Β· 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 PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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.

Β·Privacy Policy