XPM Prime Explorer symbol
XPMPrime Explorer

Block #3,242,597

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/27/2019, 2:31:20 AM Β· Difficulty 11.0027 Β· 3,593,920 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
82e1e20ec1c46a5ac4ffc754276111bc2ea2777fed7ed20b5d857808d0b5d3c7
View on Chainz β†—

Height

#3,242,597

Difficulty

11.002690

Transactions

2

Size

8.21 KB

Version

2

Bits

0b00b047

Nonce

906,654,675

Timestamp

6/27/2019, 2:31:20 AM

Confirmations

3,593,920

Mined by

⛏️ P2SHARbm48qRsZyALB7gqdgsMMKGGA9xQc8DBX

Merkle Root

3249e1382e769b824d9fc83cf475629b2eda8cafbb1e31968708782fbf035f51
Transactions (2)
Coinbase23b8af02333b07…aaeea01e539f03
1 in β†’ 1 out8.3400 XPM110 B
ARbm48qR…9xQc8DBX
a91f91367fb3f0…011c03c6706d8d
55 in β†’ 2 out1773.0334 XPM8.02 KB
AVDvwh2P…b6H33JtEANcE4iqA…f6KLuoPQ
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.

3.255 Γ— 10⁹⁷(98-digit number)
32551112620615682500…90053790801578803199
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
3.255 Γ— 10⁹⁷(98-digit number)
32551112620615682500…90053790801578803199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.255 Γ— 10⁹⁷(98-digit number)
32551112620615682500…90053790801578803201
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
6.510 Γ— 10⁹⁷(98-digit number)
65102225241231365001…80107581603157606399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.510 Γ— 10⁹⁷(98-digit number)
65102225241231365001…80107581603157606401
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
1.302 Γ— 10⁹⁸(99-digit number)
13020445048246273000…60215163206315212799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.302 Γ— 10⁹⁸(99-digit number)
13020445048246273000…60215163206315212801
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
2.604 Γ— 10⁹⁸(99-digit number)
26040890096492546000…20430326412630425599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.604 Γ— 10⁹⁸(99-digit number)
26040890096492546000…20430326412630425601
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
5.208 Γ— 10⁹⁸(99-digit number)
52081780192985092000…40860652825260851199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.208 Γ— 10⁹⁸(99-digit number)
52081780192985092000…40860652825260851201
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
1.041 Γ— 10⁹⁹(100-digit number)
10416356038597018400…81721305650521702399
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:57,936,413 XPMΒ·at block #6,836,516 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