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Block #2,745,006

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/12/2018, 1:43:00 AM Β· Difficulty 11.6464 Β· 4,097,349 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d01b2f2e2d33e6702f4a750805124cc8a625ae258c1fc230265ed69f905a0efc
View on Chainz β†—

Height

#2,745,006

Difficulty

11.646356

Transactions

2

Size

1.43 KB

Version

2

Bits

0ba5779d

Nonce

1,511,039,843

Timestamp

7/12/2018, 1:43:00 AM

Confirmations

4,097,349

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

e93a40010d9cec319e109a1903245c3c6daca9aef7fa55fdf997b69264830a4a
Transactions (2)
Coinbase219e729093faf5…a4deb8da30b5a2
1 in β†’ 1 out7.3800 XPM110 B
AZtxQr2F…7grUWrUz
67d80d3b4ade09…bdc5288a13033a
8 in β†’ 2 out9993.8600 XPM1.23 KB
AR9kUFSz…dAhVeDtLAP2U9Nxm…TK495Nur
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.

1.609 Γ— 10⁹⁢(97-digit number)
16094420086378977578…99171076709529395199
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
1.609 Γ— 10⁹⁢(97-digit number)
16094420086378977578…99171076709529395199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.609 Γ— 10⁹⁢(97-digit number)
16094420086378977578…99171076709529395201
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
3.218 Γ— 10⁹⁢(97-digit number)
32188840172757955157…98342153419058790399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.218 Γ— 10⁹⁢(97-digit number)
32188840172757955157…98342153419058790401
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
6.437 Γ— 10⁹⁢(97-digit number)
64377680345515910315…96684306838117580799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.437 Γ— 10⁹⁢(97-digit number)
64377680345515910315…96684306838117580801
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
1.287 Γ— 10⁹⁷(98-digit number)
12875536069103182063…93368613676235161599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.287 Γ— 10⁹⁷(98-digit number)
12875536069103182063…93368613676235161601
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
2.575 Γ— 10⁹⁷(98-digit number)
25751072138206364126…86737227352470323199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.575 Γ— 10⁹⁷(98-digit number)
25751072138206364126…86737227352470323201
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
5.150 Γ— 10⁹⁷(98-digit number)
51502144276412728252…73474454704940646399
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:57,983,247 XPMΒ·at block #6,842,354 Β· updates every 60s
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