XPM Prime Explorer symbol
XPMPrime Explorer

Block #181,881

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/26/2013, 9:21:36 PM Β· Difficulty 9.8599 Β· 6,628,452 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d14a5f68ce56a731bd66fb8f7963503f285e3c5f24af95d4a27a81a9be34bad8
View on Chainz β†—

Height

#181,881

Difficulty

9.859881

Transactions

1

Size

199 B

Version

2

Bits

09dc2124

Nonce

77,816

Timestamp

9/26/2013, 9:21:36 PM

Confirmations

6,628,452

Mined by

⛏️ P2SHAUm1UXE6PTt11eQB2DXhcmZJbwSTx2UrXW

Merkle Root

4249099669b6eeb8fc2c52292725a1fcb85a93b17c0124c5884712b45e49a55e
Transactions (1)
Coinbase4249099669b6ee…4712b45e49a55e
1 in β†’ 1 out10.2700 XPM109 B
AUm1UXE6…STx2UrXW
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.

4.622 Γ— 10⁹⁡(96-digit number)
46221873233010041992…67007101720805081599
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
4.622 Γ— 10⁹⁡(96-digit number)
46221873233010041992…67007101720805081599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.244 Γ— 10⁹⁡(96-digit number)
92443746466020083985…34014203441610163199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.848 Γ— 10⁹⁢(97-digit number)
18488749293204016797…68028406883220326399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.697 Γ— 10⁹⁢(97-digit number)
36977498586408033594…36056813766440652799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.395 Γ— 10⁹⁢(97-digit number)
73954997172816067188…72113627532881305599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.479 Γ— 10⁹⁷(98-digit number)
14790999434563213437…44227255065762611199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.958 Γ— 10⁹⁷(98-digit number)
29581998869126426875…88454510131525222399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.916 Γ— 10⁹⁷(98-digit number)
59163997738252853750…76909020263050444799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.183 Γ— 10⁹⁸(99-digit number)
11832799547650570750…53818040526100889599
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:57,726,744 XPMΒ·at block #6,810,332 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.
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