XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,642,444

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/1/2018, 5:53:50 PM Β· Difficulty 11.6528 Β· 4,197,787 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
45859ed08f8878f11ae6064ce15fd55374f3528f0b21a9ab7c426220794ed45a
View on Chainz β†—

Height

#2,642,444

Difficulty

11.652802

Transactions

1

Size

199 B

Version

2

Bits

0ba71e06

Nonce

292,699,663

Timestamp

5/1/2018, 5:53:50 PM

Confirmations

4,197,787

Mined by

⛏️ P2SHAMGAy7bcLRdEeFnneT96adp3X8z5wVnYiP

Merkle Root

445ec7d8042aaa4fbe83689ebe2e1d3c2b3cebb343a6e5ed70ec292d741bd407
Transactions (1)
Coinbase445ec7d8042aaa…ec292d741bd407
1 in β†’ 1 out7.3500 XPM110 B
AMGAy7bc…z5wVnYiP
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.

7.016 Γ— 10⁹¹(92-digit number)
70166539686848446812…98623447032718205239
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
7.016 Γ— 10⁹¹(92-digit number)
70166539686848446812…98623447032718205239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.016 Γ— 10⁹¹(92-digit number)
70166539686848446812…98623447032718205241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.403 Γ— 10⁹²(93-digit number)
14033307937369689362…97246894065436410479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.403 Γ— 10⁹²(93-digit number)
14033307937369689362…97246894065436410481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.806 Γ— 10⁹²(93-digit number)
28066615874739378725…94493788130872820959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.806 Γ— 10⁹²(93-digit number)
28066615874739378725…94493788130872820961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
5.613 Γ— 10⁹²(93-digit number)
56133231749478757450…88987576261745641919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.613 Γ— 10⁹²(93-digit number)
56133231749478757450…88987576261745641921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.122 Γ— 10⁹³(94-digit number)
11226646349895751490…77975152523491283839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.122 Γ— 10⁹³(94-digit number)
11226646349895751490…77975152523491283841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
2.245 Γ— 10⁹³(94-digit number)
22453292699791502980…55950305046982567679
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 Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,966,160 XPMΒ·at block #6,840,230 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