XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,683,037

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/29/2018, 1:09:35 PM Β· Difficulty 11.6908 Β· 4,156,796 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ebe760c6eb23de2f17e8a4adb39e07d68097117ea965a9c2ac6f9a61c44923f3
View on Chainz β†—

Height

#2,683,037

Difficulty

11.690781

Transactions

2

Size

4.90 KB

Version

2

Bits

0bb0d703

Nonce

58,646,860

Timestamp

5/29/2018, 1:09:35 PM

Confirmations

4,156,796

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

59aef5f4f808ce325e0654546c05771806de396b2d44a2cf73242cbdc5f136ce
Transactions (2)
Coinbase715a92b88ce0d2…d14040424a29ad
1 in β†’ 1 out7.3500 XPM110 B
Adqah8zh…1WwoHJ9t
490d4deacf2610…f6100818bb641c
32 in β†’ 2 out243.0485 XPM4.70 KB
AdUbFbQ9…MXLm2P1GAbSDStaQ…uSkpxe4W
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.

6.814 Γ— 10⁹⁢(97-digit number)
68147728396074244075…77749409438657157119
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
6.814 Γ— 10⁹⁢(97-digit number)
68147728396074244075…77749409438657157119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.814 Γ— 10⁹⁢(97-digit number)
68147728396074244075…77749409438657157121
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
1.362 Γ— 10⁹⁷(98-digit number)
13629545679214848815…55498818877314314239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.362 Γ— 10⁹⁷(98-digit number)
13629545679214848815…55498818877314314241
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
2.725 Γ— 10⁹⁷(98-digit number)
27259091358429697630…10997637754628628479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.725 Γ— 10⁹⁷(98-digit number)
27259091358429697630…10997637754628628481
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
5.451 Γ— 10⁹⁷(98-digit number)
54518182716859395260…21995275509257256959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.451 Γ— 10⁹⁷(98-digit number)
54518182716859395260…21995275509257256961
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
1.090 Γ— 10⁹⁸(99-digit number)
10903636543371879052…43990551018514513919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.090 Γ— 10⁹⁸(99-digit number)
10903636543371879052…43990551018514513921
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
2.180 Γ— 10⁹⁸(99-digit number)
21807273086743758104…87981102037029027839
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:57,962,961 XPMΒ·at block #6,839,832 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