XPM Prime Explorer symbol
XPMPrime Explorer

Block #171,423

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/19/2013, 11:55:18 AM Β· Difficulty 9.8642 Β· 6,655,691 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1c34fa76348b9059ced400a9d1c7813c69865c6b719fb1e05f9e15495a5df060
View on Chainz β†—

Height

#171,423

Difficulty

9.864235

Transactions

1

Size

199 B

Version

2

Bits

09dd3e81

Nonce

6,353

Timestamp

9/19/2013, 11:55:18 AM

Confirmations

6,655,691

Mined by

⛏️ P2SHAMwAeZ2SEPtUtw6q17SQMHswQtPfb2wYuw

Merkle Root

b7acbc9da0cd86c799d8844f7c5eed4b006bf324984c1e8ed1a830be9197dcdc
Transactions (1)
Coinbaseb7acbc9da0cd86…a830be9197dcdc
1 in β†’ 1 out10.2600 XPM109 B
AMwAeZ2S…Pfb2wYuw
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.

2.628 Γ— 10⁹⁴(95-digit number)
26284839474162952231…56197434615128185161
Discovered Prime Numbers
p_k = 2^k Γ— 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
2.628 Γ— 10⁹⁴(95-digit number)
26284839474162952231…56197434615128185161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.256 Γ— 10⁹⁴(95-digit number)
52569678948325904463…12394869230256370321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.051 Γ— 10⁹⁡(96-digit number)
10513935789665180892…24789738460512740641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.102 Γ— 10⁹⁡(96-digit number)
21027871579330361785…49579476921025481281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.205 Γ— 10⁹⁡(96-digit number)
42055743158660723570…99158953842050962561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.411 Γ— 10⁹⁡(96-digit number)
84111486317321447141…98317907684101925121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.682 Γ— 10⁹⁢(97-digit number)
16822297263464289428…96635815368203850241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.364 Γ— 10⁹⁢(97-digit number)
33644594526928578856…93271630736407700481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.728 Γ— 10⁹⁢(97-digit number)
67289189053857157712…86543261472815400961
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,861,091 XPMΒ·at block #6,827,113 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