XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,087,047

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/25/2017, 10:09:45 AM Β· Difficulty 10.8740 Β· 4,745,537 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3bac8e0e81dc8fd2391ba07d4632e851fa014349f8dc82bdd650751580184916
View on Chainz β†—

Height

#2,087,047

Difficulty

10.873978

Transactions

2

Size

1.68 KB

Version

2

Bits

0adfbd0c

Nonce

1,101,886,758

Timestamp

4/25/2017, 10:09:45 AM

Confirmations

4,745,537

Mined by

⛏️ P2SHAGcEjC1Q9UZGQuyHkPGd7SmTirjuRZYMDT

Merkle Root

ac8e10a3e982a4aa8462d5db9b96978f3052af18fb5fb085d163603d7afe10f8
Transactions (2)
Coinbase0ba10165156f5c…2333b870433787
1 in β†’ 1 out8.4600 XPM109 B
AGcEjC1Q…juRZYMDT
7ae04c979ca373…5e6dac037213a5
10 in β†’ 1 out3249.8659 XPM1.49 KB
AYoy228q…feZqXfNq
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.

2.515 Γ— 10⁹³(94-digit number)
25155235501978148880…75966548120399768999
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
2.515 Γ— 10⁹³(94-digit number)
25155235501978148880…75966548120399768999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.515 Γ— 10⁹³(94-digit number)
25155235501978148880…75966548120399769001
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
5.031 Γ— 10⁹³(94-digit number)
50310471003956297761…51933096240799537999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.031 Γ— 10⁹³(94-digit number)
50310471003956297761…51933096240799538001
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
1.006 Γ— 10⁹⁴(95-digit number)
10062094200791259552…03866192481599075999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.006 Γ— 10⁹⁴(95-digit number)
10062094200791259552…03866192481599076001
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
2.012 Γ— 10⁹⁴(95-digit number)
20124188401582519104…07732384963198151999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.012 Γ— 10⁹⁴(95-digit number)
20124188401582519104…07732384963198152001
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
4.024 Γ— 10⁹⁴(95-digit number)
40248376803165038209…15464769926396303999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.024 Γ— 10⁹⁴(95-digit number)
40248376803165038209…15464769926396304001
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
8.049 Γ— 10⁹⁴(95-digit number)
80496753606330076418…30929539852792607999
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:57,904,820 XPMΒ·at block #6,832,583 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