XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,575,378

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/20/2018, 6:11:09 AM Β· Difficulty 10.9955 Β· 4,267,794 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4915d766abc5446df9e79f622779a60b41fac0bc52a6a9c2a5deb88eb1504bb1
View on Chainz β†—

Height

#2,575,378

Difficulty

10.995501

Transactions

1

Size

201 B

Version

2

Bits

0afed926

Nonce

163,401,242

Timestamp

3/20/2018, 6:11:09 AM

Confirmations

4,267,794

Mined by

⛏️ P2SHAMyGP3vyi65jXiLEMjKMqWExPGyn9EWsfk

Merkle Root

31fb9819ef578fcc5938b282633b1332f067462aeb0a573d1739ebc2a193d321
Transactions (1)
Coinbase31fb9819ef578f…39ebc2a193d321
1 in β†’ 1 out8.2600 XPM110 B
AMyGP3vy…yn9EWsfk
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.

2.804 Γ— 10⁹⁢(97-digit number)
28045964251276557959…83176245461339596799
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
2.804 Γ— 10⁹⁢(97-digit number)
28045964251276557959…83176245461339596799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.804 Γ— 10⁹⁢(97-digit number)
28045964251276557959…83176245461339596801
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
5.609 Γ— 10⁹⁢(97-digit number)
56091928502553115919…66352490922679193599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.609 Γ— 10⁹⁢(97-digit number)
56091928502553115919…66352490922679193601
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
1.121 Γ— 10⁹⁷(98-digit number)
11218385700510623183…32704981845358387199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.121 Γ— 10⁹⁷(98-digit number)
11218385700510623183…32704981845358387201
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
2.243 Γ— 10⁹⁷(98-digit number)
22436771401021246367…65409963690716774399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.243 Γ— 10⁹⁷(98-digit number)
22436771401021246367…65409963690716774401
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
4.487 Γ— 10⁹⁷(98-digit number)
44873542802042492735…30819927381433548799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.487 Γ— 10⁹⁷(98-digit number)
44873542802042492735…30819927381433548801
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
8.974 Γ— 10⁹⁷(98-digit number)
89747085604084985471…61639854762867097599
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:57,989,742 XPMΒ·at block #6,843,171 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