XPM Prime Explorer symbol
XPMPrime Explorer

Block #172,674

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/20/2013, 10:25:25 AM Β· Difficulty 9.8617 Β· 6,635,228 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
60b588ebbd56a54d2f3455cef200e6d3851cc018c1c9f71e760fe28b3b9c1fa5
View on Chainz β†—

Height

#172,674

Difficulty

9.861713

Transactions

2

Size

425 B

Version

2

Bits

09dc9932

Nonce

224,025

Timestamp

9/20/2013, 10:25:25 AM

Confirmations

6,635,228

Mined by

⛏️ P2SHANB7PfrLf8wUyfx97cFPU6XkrJCNt513wc

Merkle Root

a8eefd0211e736ad44ed51312702d2c19060f37c4e85e1e154c861888b7ed68e
Transactions (2)
Coinbased28155b429def4…397e665f9600ad
1 in β†’ 1 out10.2800 XPM109 B
ANB7PfrL…CNt513wc
b7a4b44ff36956…83a719b76cf4b9
1 in β†’ 2 out6.1866 XPM227 B
AagQPgpy…1pSGhdMjAMqy1Z9q…9qLErWJg
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.

3.270 Γ— 10⁹²(93-digit number)
32700386842580377067…26135959304785948341
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
3.270 Γ— 10⁹²(93-digit number)
32700386842580377067…26135959304785948341
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.540 Γ— 10⁹²(93-digit number)
65400773685160754134…52271918609571896681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.308 Γ— 10⁹³(94-digit number)
13080154737032150826…04543837219143793361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.616 Γ— 10⁹³(94-digit number)
26160309474064301653…09087674438287586721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.232 Γ— 10⁹³(94-digit number)
52320618948128603307…18175348876575173441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.046 Γ— 10⁹⁴(95-digit number)
10464123789625720661…36350697753150346881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.092 Γ— 10⁹⁴(95-digit number)
20928247579251441323…72701395506300693761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.185 Γ— 10⁹⁴(95-digit number)
41856495158502882646…45402791012601387521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.371 Γ— 10⁹⁴(95-digit number)
83712990317005765292…90805582025202775041
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:57,707,249 XPMΒ·at block #6,807,901 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