XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,696,021

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/7/2018, 6:54:38 PM Β· Difficulty 11.6708 Β· 4,145,973 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
de82d5b466bab99b169808c7f74228916391ca6425db9d3413f20468efb90ced
View on Chainz β†—

Height

#2,696,021

Difficulty

11.670762

Transactions

2

Size

539 B

Version

2

Bits

0babb70d

Nonce

769,235,494

Timestamp

6/7/2018, 6:54:38 PM

Confirmations

4,145,973

Mined by

⛏️ P2SHAZk2Tv5c7HsvFnX7jwGAU8hCCeSx6xUbA9

Merkle Root

973d0992f094a77d1c82ff1ffc678dcdd2c86a6ddcd1682faa99efdc7fc23568
Transactions (2)
Coinbasead8b2ad3e16ec3…61f241596c038e
1 in β†’ 1 out7.3400 XPM109 B
AZk2Tv5c…Sx6xUbA9
6e62008011e780…72fbf7a024b484
2 in β†’ 1 out7.9900 XPM340 B
ASVLgTSP…eFPhvU7R
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.

1.144 Γ— 10⁹⁡(96-digit number)
11440671973866886055…84289825593999884801
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
1.144 Γ— 10⁹⁡(96-digit number)
11440671973866886055…84289825593999884801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.288 Γ— 10⁹⁡(96-digit number)
22881343947733772111…68579651187999769601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.576 Γ— 10⁹⁡(96-digit number)
45762687895467544222…37159302375999539201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.152 Γ— 10⁹⁡(96-digit number)
91525375790935088444…74318604751999078401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.830 Γ— 10⁹⁢(97-digit number)
18305075158187017688…48637209503998156801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.661 Γ— 10⁹⁢(97-digit number)
36610150316374035377…97274419007996313601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.322 Γ— 10⁹⁢(97-digit number)
73220300632748070755…94548838015992627201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.464 Γ— 10⁹⁷(98-digit number)
14644060126549614151…89097676031985254401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.928 Γ— 10⁹⁷(98-digit number)
29288120253099228302…78195352063970508801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.857 Γ— 10⁹⁷(98-digit number)
58576240506198456604…56390704127941017601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.171 Γ— 10⁹⁸(99-digit number)
11715248101239691320…12781408255882035201
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:57,980,340 XPMΒ·at block #6,841,993 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