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Block #2,751,523

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/16/2018, 3:13:29 PM Β· Difficulty 11.6429 Β· 4,091,576 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5bd7dca967e06c130375049e602ff25850ffa4708867436a20912d5e6a606588
View on Chainz β†—

Height

#2,751,523

Difficulty

11.642859

Transactions

2

Size

16.31 KB

Version

2

Bits

0ba4926e

Nonce

1,502,570,842

Timestamp

7/16/2018, 3:13:29 PM

Confirmations

4,091,576

Mined by

⛏️ P2SHAKvj7mW7h1YhmTKn1XuJ7Xg6zLP7Wt2afo

Merkle Root

3ba5b865c5c04b1f9633bb0e5120ae211c336430839ca4f10f56f3a86dd29915
Transactions (2)
Coinbase414d44386826fa…7e0f586f97b06d
1 in β†’ 1 out7.5300 XPM110 B
AKvj7mW7…P7Wt2afo
1a0266469b956c…0e3e6a56d696d5
111 in β†’ 2 out440.7100 XPM16.11 KB
AdLKy4sk…QtnV8wnPAQRn6yfR…z5FsKtdj
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.

3.141 Γ— 10⁹⁷(98-digit number)
31410438000934158608…70718656330431257599
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
3.141 Γ— 10⁹⁷(98-digit number)
31410438000934158608…70718656330431257599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.141 Γ— 10⁹⁷(98-digit number)
31410438000934158608…70718656330431257601
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
6.282 Γ— 10⁹⁷(98-digit number)
62820876001868317216…41437312660862515199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.282 Γ— 10⁹⁷(98-digit number)
62820876001868317216…41437312660862515201
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
1.256 Γ— 10⁹⁸(99-digit number)
12564175200373663443…82874625321725030399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.256 Γ— 10⁹⁸(99-digit number)
12564175200373663443…82874625321725030401
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
2.512 Γ— 10⁹⁸(99-digit number)
25128350400747326886…65749250643450060799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.512 Γ— 10⁹⁸(99-digit number)
25128350400747326886…65749250643450060801
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
5.025 Γ— 10⁹⁸(99-digit number)
50256700801494653773…31498501286900121599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.025 Γ— 10⁹⁸(99-digit number)
50256700801494653773…31498501286900121601
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
1.005 Γ— 10⁹⁹(100-digit number)
10051340160298930754…62997002573800243199
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:57,989,155 XPMΒ·at block #6,843,098 Β· updates every 60s
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