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Block #2,643,396

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/2/2018, 2:23:13 AM Β· Difficulty 11.6820 Β· 4,198,771 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ae1a38ef478460d0bbd77ad8f10d1863e560a2ef29ea5bc763166869435231ef
View on Chainz β†—

Height

#2,643,396

Difficulty

11.682031

Transactions

1

Size

199 B

Version

2

Bits

0bae9999

Nonce

309,960,618

Timestamp

5/2/2018, 2:23:13 AM

Confirmations

4,198,771

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

2939e3f746bfe093c9c0a6edd8cf3b4fe5baac5901687eac23ca6dab2cc288b1
Transactions (1)
Coinbase2939e3f746bfe0…ca6dab2cc288b1
1 in β†’ 1 out7.3200 XPM110 B
Adqah8zh…1WwoHJ9t
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.

4.360 Γ— 10⁹²(93-digit number)
43601973670382801123…49779158705067360759
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
4.360 Γ— 10⁹²(93-digit number)
43601973670382801123…49779158705067360759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.360 Γ— 10⁹²(93-digit number)
43601973670382801123…49779158705067360761
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
8.720 Γ— 10⁹²(93-digit number)
87203947340765602246…99558317410134721519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.720 Γ— 10⁹²(93-digit number)
87203947340765602246…99558317410134721521
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
1.744 Γ— 10⁹³(94-digit number)
17440789468153120449…99116634820269443039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.744 Γ— 10⁹³(94-digit number)
17440789468153120449…99116634820269443041
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
3.488 Γ— 10⁹³(94-digit number)
34881578936306240898…98233269640538886079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.488 Γ— 10⁹³(94-digit number)
34881578936306240898…98233269640538886081
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
6.976 Γ— 10⁹³(94-digit number)
69763157872612481797…96466539281077772159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.976 Γ— 10⁹³(94-digit number)
69763157872612481797…96466539281077772161
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
1.395 Γ— 10⁹⁴(95-digit number)
13952631574522496359…92933078562155544319
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:57,981,727 XPMΒ·at block #6,842,166 Β· updates every 60s
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