XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,731,325

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/2/2018, 5:05:15 PM Β· Difficulty 11.6313 Β· 4,110,281 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
664a2b713e13be094a970bfb6f369d359d63edd33b465ce4841652e0eca48553
View on Chainz β†—

Height

#2,731,325

Difficulty

11.631272

Transactions

1

Size

200 B

Version

2

Bits

0ba19b0d

Nonce

184,829,824

Timestamp

7/2/2018, 5:05:15 PM

Confirmations

4,110,281

Mined by

⛏️ P2SHAPeWHmLGSH2bXiaVbeLFGwHXU9CA6JgaQE

Merkle Root

bdbb2115d611a96717cb12383be0706f0258794d375ba87949f66483fe15edea
Transactions (1)
Coinbasebdbb2115d611a9…f66483fe15edea
1 in β†’ 1 out7.3800 XPM110 B
APeWHmLG…CA6JgaQE
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.

8.026 Γ— 10⁹⁴(95-digit number)
80269633086006589540…22717943340185529921
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
8.026 Γ— 10⁹⁴(95-digit number)
80269633086006589540…22717943340185529921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.605 Γ— 10⁹⁡(96-digit number)
16053926617201317908…45435886680371059841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.210 Γ— 10⁹⁡(96-digit number)
32107853234402635816…90871773360742119681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.421 Γ— 10⁹⁡(96-digit number)
64215706468805271632…81743546721484239361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.284 Γ— 10⁹⁢(97-digit number)
12843141293761054326…63487093442968478721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.568 Γ— 10⁹⁢(97-digit number)
25686282587522108652…26974186885936957441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.137 Γ— 10⁹⁢(97-digit number)
51372565175044217305…53948373771873914881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.027 Γ— 10⁹⁷(98-digit number)
10274513035008843461…07896747543747829761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.054 Γ— 10⁹⁷(98-digit number)
20549026070017686922…15793495087495659521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.109 Γ— 10⁹⁷(98-digit number)
41098052140035373844…31586990174991319041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.219 Γ— 10⁹⁷(98-digit number)
82196104280070747689…63173980349982638081
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,977,235 XPMΒ·at block #6,841,605 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