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Block #2,680,325

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/27/2018, 3:37:14 PM Β· Difficulty 11.6918 Β· 4,157,355 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
93261ee038ac34f0131744e590cf432e190b8e6793cb8636be0bf26352a61e86
View on Chainz β†—

Height

#2,680,325

Difficulty

11.691819

Transactions

1

Size

200 B

Version

2

Bits

0bb11b12

Nonce

141,289,680

Timestamp

5/27/2018, 3:37:14 PM

Confirmations

4,157,355

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

7ac08a126571016c057ceae397136e0a3c543d2e6605db9c83718b0cf949d189
Transactions (1)
Coinbase7ac08a12657101…718b0cf949d189
1 in β†’ 1 out7.3000 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.

9.806 Γ— 10⁹⁴(95-digit number)
98067023716158737420…60082339449869846719
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
9.806 Γ— 10⁹⁴(95-digit number)
98067023716158737420…60082339449869846719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.806 Γ— 10⁹⁴(95-digit number)
98067023716158737420…60082339449869846721
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
1.961 Γ— 10⁹⁡(96-digit number)
19613404743231747484…20164678899739693439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.961 Γ— 10⁹⁡(96-digit number)
19613404743231747484…20164678899739693441
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
3.922 Γ— 10⁹⁡(96-digit number)
39226809486463494968…40329357799479386879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.922 Γ— 10⁹⁡(96-digit number)
39226809486463494968…40329357799479386881
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
7.845 Γ— 10⁹⁡(96-digit number)
78453618972926989936…80658715598958773759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.845 Γ— 10⁹⁡(96-digit number)
78453618972926989936…80658715598958773761
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
1.569 Γ— 10⁹⁢(97-digit number)
15690723794585397987…61317431197917547519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.569 Γ— 10⁹⁢(97-digit number)
15690723794585397987…61317431197917547521
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
3.138 Γ— 10⁹⁢(97-digit number)
31381447589170795974…22634862395835095039
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:57,945,765 XPMΒ·at block #6,837,679 Β· updates every 60s
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