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Block #2,095,716

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/1/2017, 12:24:24 PM Β· Difficulty 10.8715 Β· 4,730,859 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5ee1f5416a4cf181fca0c83276e35dc42965daaa4c242b5fda62ff938d178662
View on Chainz β†—

Height

#2,095,716

Difficulty

10.871546

Transactions

2

Size

1.57 KB

Version

2

Bits

0adf1daa

Nonce

305,342,363

Timestamp

5/1/2017, 12:24:24 PM

Confirmations

4,730,859

Mined by

⛏️ P2SHAR7erK5wL1Prkb1Bxw1ACawYuNQ8h2iG79

Merkle Root

db314cf78fd0d32da0c0cff545e0f1a5f86c7f3dfe9705449712633bb19a3a2e
Transactions (2)
Coinbased9c95c577d6ded…fc3954c74e5e62
1 in β†’ 1 out8.4700 XPM110 B
AR7erK5w…Q8h2iG79
a400115ba0eee6…459057ea41f652
9 in β†’ 2 out3605.6429 XPM1.37 KB
ALATMSeJ…BePBe22VAbAEE55B…t9uajDaq
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.

4.366 Γ— 10⁹⁴(95-digit number)
43668722876253808830…19924554724810634639
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
4.366 Γ— 10⁹⁴(95-digit number)
43668722876253808830…19924554724810634639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.366 Γ— 10⁹⁴(95-digit number)
43668722876253808830…19924554724810634641
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
8.733 Γ— 10⁹⁴(95-digit number)
87337445752507617661…39849109449621269279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.733 Γ— 10⁹⁴(95-digit number)
87337445752507617661…39849109449621269281
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
1.746 Γ— 10⁹⁡(96-digit number)
17467489150501523532…79698218899242538559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.746 Γ— 10⁹⁡(96-digit number)
17467489150501523532…79698218899242538561
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
3.493 Γ— 10⁹⁡(96-digit number)
34934978301003047064…59396437798485077119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.493 Γ— 10⁹⁡(96-digit number)
34934978301003047064…59396437798485077121
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
6.986 Γ— 10⁹⁡(96-digit number)
69869956602006094129…18792875596970154239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.986 Γ— 10⁹⁡(96-digit number)
69869956602006094129…18792875596970154241
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:57,856,749 XPMΒ·at block #6,826,574 Β· updates every 60s
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