XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,743,493

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/11/2018, 2:36:03 AM Β· Difficulty 11.6373 Β· 4,088,131 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0abcb2fc83c39d2f193b197f3c21be769ebf59e1dd4bbceaa6039661715d0823
View on Chainz β†—

Height

#2,743,493

Difficulty

11.637339

Transactions

2

Size

1.28 KB

Version

2

Bits

0ba328a0

Nonce

1,270,296,680

Timestamp

7/11/2018, 2:36:03 AM

Confirmations

4,088,131

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

3783dd4d8cd9ac9a5f79c32b2ad9a0b263e24a76ff7ce27cfe392f9e4133b40d
Transactions (2)
Coinbase84ab262a972908…fe9fc2a84a69f6
1 in β†’ 1 out7.3900 XPM110 B
AZtxQr2F…7grUWrUz
7899392a841c77…653e7755528bdf
7 in β†’ 2 out456.4200 XPM1.09 KB
AbiZw7N1…HPacQJfkAQjsmK6K…MyCcnxmT
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.

4.481 Γ— 10⁹⁡(96-digit number)
44810566462988168872…60706814605267779201
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
4.481 Γ— 10⁹⁡(96-digit number)
44810566462988168872…60706814605267779201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.962 Γ— 10⁹⁡(96-digit number)
89621132925976337744…21413629210535558401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.792 Γ— 10⁹⁢(97-digit number)
17924226585195267548…42827258421071116801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.584 Γ— 10⁹⁢(97-digit number)
35848453170390535097…85654516842142233601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.169 Γ— 10⁹⁢(97-digit number)
71696906340781070195…71309033684284467201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.433 Γ— 10⁹⁷(98-digit number)
14339381268156214039…42618067368568934401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.867 Γ— 10⁹⁷(98-digit number)
28678762536312428078…85236134737137868801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.735 Γ— 10⁹⁷(98-digit number)
57357525072624856156…70472269474275737601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.147 Γ— 10⁹⁸(99-digit number)
11471505014524971231…40944538948551475201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.294 Γ— 10⁹⁸(99-digit number)
22943010029049942462…81889077897102950401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.588 Γ— 10⁹⁸(99-digit number)
45886020058099884925…63778155794205900801
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:57,897,093 XPMΒ·at block #6,831,623 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