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Block #2,845,795

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/19/2018, 3:53:17 AM Β· Difficulty 11.7296 Β· 3,993,612 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b0d276600c8a21729c4b19957c76c8c2fbfcb9bec6cabc658e2ba862ac279222
View on Chainz β†—

Height

#2,845,795

Difficulty

11.729608

Transactions

1

Size

199 B

Version

2

Bits

0bbac796

Nonce

372,896,911

Timestamp

9/19/2018, 3:53:17 AM

Confirmations

3,993,612

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

8a10a8005d7cfeed5328dabb8a08aa76e5762a71f2120410db50c16479f6b9f2
Transactions (1)
Coinbase8a10a8005d7cfe…50c16479f6b9f2
1 in β†’ 1 out7.2600 XPM110 B
AZtxQr2F…7grUWrUz
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.

2.361 Γ— 10⁹³(94-digit number)
23612439937032782256…27069480995997823999
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
2.361 Γ— 10⁹³(94-digit number)
23612439937032782256…27069480995997823999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.361 Γ— 10⁹³(94-digit number)
23612439937032782256…27069480995997824001
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
4.722 Γ— 10⁹³(94-digit number)
47224879874065564512…54138961991995647999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.722 Γ— 10⁹³(94-digit number)
47224879874065564512…54138961991995648001
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
9.444 Γ— 10⁹³(94-digit number)
94449759748131129025…08277923983991295999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.444 Γ— 10⁹³(94-digit number)
94449759748131129025…08277923983991296001
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
1.888 Γ— 10⁹⁴(95-digit number)
18889951949626225805…16555847967982591999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.888 Γ— 10⁹⁴(95-digit number)
18889951949626225805…16555847967982592001
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
3.777 Γ— 10⁹⁴(95-digit number)
37779903899252451610…33111695935965183999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.777 Γ— 10⁹⁴(95-digit number)
37779903899252451610…33111695935965184001
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
7.555 Γ— 10⁹⁴(95-digit number)
75559807798504903220…66223391871930367999
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:57,959,543 XPMΒ·at block #6,839,406 Β· updates every 60s
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