XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,576,479

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/20/2018, 8:53:38 PM Β· Difficulty 10.9957 Β· 4,268,337 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
34437c980864998f544169763d3de7ebaf5109785d04488ed039c86b365b7277
View on Chainz β†—

Height

#2,576,479

Difficulty

10.995723

Transactions

1

Size

200 B

Version

2

Bits

0afee7bb

Nonce

976,258,110

Timestamp

3/20/2018, 8:53:38 PM

Confirmations

4,268,337

Mined by

⛏️ P2SHASkJdMuTFATAzcniCUYiesWMzagiyuLj3b

Merkle Root

0ca71ca1ff140c36d522fb8440cde7c0c74213f5a15a57ed1dc7e7430a52f088
Transactions (1)
Coinbase0ca71ca1ff140c…c7e7430a52f088
1 in β†’ 1 out8.2600 XPM109 B
ASkJdMuT…giyuLj3b
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.

5.255 Γ— 10⁹⁷(98-digit number)
52552150983867694740…31292294551279042559
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
5.255 Γ— 10⁹⁷(98-digit number)
52552150983867694740…31292294551279042559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.255 Γ— 10⁹⁷(98-digit number)
52552150983867694740…31292294551279042561
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
1.051 Γ— 10⁹⁸(99-digit number)
10510430196773538948…62584589102558085119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.051 Γ— 10⁹⁸(99-digit number)
10510430196773538948…62584589102558085121
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
2.102 Γ— 10⁹⁸(99-digit number)
21020860393547077896…25169178205116170239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.102 Γ— 10⁹⁸(99-digit number)
21020860393547077896…25169178205116170241
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
4.204 Γ— 10⁹⁸(99-digit number)
42041720787094155792…50338356410232340479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.204 Γ— 10⁹⁸(99-digit number)
42041720787094155792…50338356410232340481
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
8.408 Γ— 10⁹⁸(99-digit number)
84083441574188311584…00676712820464680959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.408 Γ— 10⁹⁸(99-digit number)
84083441574188311584…00676712820464680961
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
1.681 Γ— 10⁹⁹(100-digit number)
16816688314837662316…01353425640929361919
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:58,002,935 XPMΒ·at block #6,844,815 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