XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,700,780

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/11/2018, 10:44:01 AM Β· Difficulty 11.6359 Β· 4,133,026 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
52dc91f98f2fa7dd19d1c6bba753f75c1917b61931de702354c39622907b1853
View on Chainz β†—

Height

#2,700,780

Difficulty

11.635859

Transactions

1

Size

201 B

Version

2

Bits

0ba2c7a6

Nonce

282,885,647

Timestamp

6/11/2018, 10:44:01 AM

Confirmations

4,133,026

Mined by

⛏️ P2SHARzaUmuw4oWKjubezE5ATJ6JunJyUvvyE3

Merkle Root

2baba2583c9a8e7ee5e50db1cfe27fc93ad955e72e93456c247d1dd9de3807ff
Transactions (1)
Coinbase2baba2583c9a8e…7d1dd9de3807ff
1 in β†’ 1 out7.3700 XPM110 B
ARzaUmuw…JyUvvyE3
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.

4.388 Γ— 10⁹⁢(97-digit number)
43883750946599992717…13144310582521414399
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
4.388 Γ— 10⁹⁢(97-digit number)
43883750946599992717…13144310582521414399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.388 Γ— 10⁹⁢(97-digit number)
43883750946599992717…13144310582521414401
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
8.776 Γ— 10⁹⁢(97-digit number)
87767501893199985434…26288621165042828799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.776 Γ— 10⁹⁢(97-digit number)
87767501893199985434…26288621165042828801
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
1.755 Γ— 10⁹⁷(98-digit number)
17553500378639997086…52577242330085657599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.755 Γ— 10⁹⁷(98-digit number)
17553500378639997086…52577242330085657601
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
3.510 Γ— 10⁹⁷(98-digit number)
35107000757279994173…05154484660171315199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.510 Γ— 10⁹⁷(98-digit number)
35107000757279994173…05154484660171315201
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
7.021 Γ— 10⁹⁷(98-digit number)
70214001514559988347…10308969320342630399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.021 Γ— 10⁹⁷(98-digit number)
70214001514559988347…10308969320342630401
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
1.404 Γ— 10⁹⁸(99-digit number)
14042800302911997669…20617938640685260799
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:57,914,671 XPMΒ·at block #6,833,805 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