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Block #2,095,375

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/1/2017, 6:09:38 AM Β· Difficulty 10.8724 Β· 4,737,165 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2528e8c893ad87b3df873cad10acd3a686b38c5b115482894d0ca9891a16e80a
View on Chainz β†—

Height

#2,095,375

Difficulty

10.872401

Transactions

1

Size

200 B

Version

2

Bits

0adf55a7

Nonce

932,636,998

Timestamp

5/1/2017, 6:09:38 AM

Confirmations

4,737,165

Mined by

⛏️ P2SHAeKpUXBiex85rUYWr7zKVKUXN4iQ4aUfP4

Merkle Root

c158cf9a636f68951c8cd49b238a0c815cd951bc8a9c2e85aaac6c0c7d1c6fb6
Transactions (1)
Coinbasec158cf9a636f68…ac6c0c7d1c6fb6
1 in β†’ 1 out8.4500 XPM110 B
AeKpUXBi…iQ4aUfP4
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.

1.723 Γ— 10⁹⁡(96-digit number)
17230378982771846501…50236260726674401599
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
1.723 Γ— 10⁹⁡(96-digit number)
17230378982771846501…50236260726674401599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.723 Γ— 10⁹⁡(96-digit number)
17230378982771846501…50236260726674401601
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
3.446 Γ— 10⁹⁡(96-digit number)
34460757965543693002…00472521453348803199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.446 Γ— 10⁹⁡(96-digit number)
34460757965543693002…00472521453348803201
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
6.892 Γ— 10⁹⁡(96-digit number)
68921515931087386004…00945042906697606399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.892 Γ— 10⁹⁡(96-digit number)
68921515931087386004…00945042906697606401
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
1.378 Γ— 10⁹⁢(97-digit number)
13784303186217477200…01890085813395212799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.378 Γ— 10⁹⁢(97-digit number)
13784303186217477200…01890085813395212801
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
2.756 Γ— 10⁹⁢(97-digit number)
27568606372434954401…03780171626790425599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.756 Γ— 10⁹⁢(97-digit number)
27568606372434954401…03780171626790425601
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:57,904,482 XPMΒ·at block #6,832,539 Β· updates every 60s
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