XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,148,888

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/6/2017, 6:04:25 PM Β· Difficulty 10.8962 Β· 4,692,702 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4e356f51f5302c197fe3de80785cf94a9e2a1b247f1e52edb26c4cad83e023e0
View on Chainz β†—

Height

#2,148,888

Difficulty

10.896203

Transactions

2

Size

427 B

Version

2

Bits

0ae56d89

Nonce

194,358,481

Timestamp

6/6/2017, 6:04:25 PM

Confirmations

4,692,702

Mined by

⛏️ P2SHAG46bH3V11joRhkLfNWBpCiQrXzXSd4pfg

Merkle Root

f399c2ed2d97313884170c75478d26fa07be8f931b4d78d4e7a57ad5e3eca694
Transactions (2)
Coinbase0a05dc517ea442…074bf2ed50443c
1 in β†’ 1 out8.4200 XPM110 B
AG46bH3V…zXSd4pfg
786f8a68c7d882…ddd68bdf74be46
1 in β†’ 2 out123063.5835 XPM227 B
ARzXxLeJ…xwwq1PEzAMNqyy2W…ise9w8w1
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.

1.028 Γ— 10⁹⁴(95-digit number)
10285955986600367769…64420471229531504399
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
1.028 Γ— 10⁹⁴(95-digit number)
10285955986600367769…64420471229531504399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.028 Γ— 10⁹⁴(95-digit number)
10285955986600367769…64420471229531504401
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
2.057 Γ— 10⁹⁴(95-digit number)
20571911973200735539…28840942459063008799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.057 Γ— 10⁹⁴(95-digit number)
20571911973200735539…28840942459063008801
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
4.114 Γ— 10⁹⁴(95-digit number)
41143823946401471079…57681884918126017599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.114 Γ— 10⁹⁴(95-digit number)
41143823946401471079…57681884918126017601
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
8.228 Γ— 10⁹⁴(95-digit number)
82287647892802942158…15363769836252035199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.228 Γ— 10⁹⁴(95-digit number)
82287647892802942158…15363769836252035201
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
1.645 Γ— 10⁹⁡(96-digit number)
16457529578560588431…30727539672504070399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.645 Γ— 10⁹⁡(96-digit number)
16457529578560588431…30727539672504070401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,977,107 XPMΒ·at block #6,841,589 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