XPM Prime Explorer symbol
XPMPrime Explorer

Block #105,559

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/8/2013, 2:12:20 PM Β· Difficulty 9.5870 Β· 6,709,495 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
94be31a98db96663c5a3d90a9733a6ac5e585d7f5fc500805d4c8284c92c1b97
View on Chainz β†—

Height

#105,559

Difficulty

9.587022

Transactions

1

Size

199 B

Version

2

Bits

09964716

Nonce

32,161

Timestamp

8/8/2013, 2:12:20 PM

Confirmations

6,709,495

Mined by

⛏️ P2SHAXvMMum1Pa5kWMWJFC5uKC4CTEy1ajpFRb

Merkle Root

e397ee74bd9fd2e0b041f047058d9d8427487dcd8130e73a709cb2a13cfede3d
Transactions (1)
Coinbasee397ee74bd9fd2…9cb2a13cfede3d
1 in β†’ 1 out10.8600 XPM109 B
AXvMMum1…y1ajpFRb
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.

3.174 Γ— 10⁹⁴(95-digit number)
31743333720730114039…48821845015384360849
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
3.174 Γ— 10⁹⁴(95-digit number)
31743333720730114039…48821845015384360849
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.348 Γ— 10⁹⁴(95-digit number)
63486667441460228079…97643690030768721699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.269 Γ— 10⁹⁡(96-digit number)
12697333488292045615…95287380061537443399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.539 Γ— 10⁹⁡(96-digit number)
25394666976584091231…90574760123074886799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.078 Γ— 10⁹⁡(96-digit number)
50789333953168182463…81149520246149773599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.015 Γ— 10⁹⁢(97-digit number)
10157866790633636492…62299040492299547199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.031 Γ— 10⁹⁢(97-digit number)
20315733581267272985…24598080984599094399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.063 Γ— 10⁹⁢(97-digit number)
40631467162534545970…49196161969198188799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.126 Γ— 10⁹⁢(97-digit number)
81262934325069091941…98392323938396377599
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:57,764,522 XPMΒ·at block #6,815,053 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