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Block #2,643,006

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/1/2018, 10:53:46 PM Β· Difficulty 11.6704 Β· 4,197,330 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1b9fa3e486e3788227006c5953a3c069e4e2f32fe305ee4de70ca28316e855f4
View on Chainz β†—

Height

#2,643,006

Difficulty

11.670403

Transactions

1

Size

200 B

Version

2

Bits

0bab9f8f

Nonce

257,713,372

Timestamp

5/1/2018, 10:53:46 PM

Confirmations

4,197,330

Mined by

⛏️ P2SHAXYyYDWF3uZXz9F5ZLndXkYBLpfDtbEFMt

Merkle Root

d6232f0aeb828eb1dee4a192f98ccb4987e1162bc4b77bad4e4becd18908b44f
Transactions (1)
Coinbased6232f0aeb828e…4becd18908b44f
1 in β†’ 1 out7.3300 XPM110 B
AXYyYDWF…fDtbEFMt
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.

3.135 Γ— 10⁹⁴(95-digit number)
31359497734602411020…85011231136230830079
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
3.135 Γ— 10⁹⁴(95-digit number)
31359497734602411020…85011231136230830079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.135 Γ— 10⁹⁴(95-digit number)
31359497734602411020…85011231136230830081
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
6.271 Γ— 10⁹⁴(95-digit number)
62718995469204822040…70022462272461660159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.271 Γ— 10⁹⁴(95-digit number)
62718995469204822040…70022462272461660161
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
1.254 Γ— 10⁹⁡(96-digit number)
12543799093840964408…40044924544923320319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.254 Γ— 10⁹⁡(96-digit number)
12543799093840964408…40044924544923320321
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
2.508 Γ— 10⁹⁡(96-digit number)
25087598187681928816…80089849089846640639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.508 Γ— 10⁹⁡(96-digit number)
25087598187681928816…80089849089846640641
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
5.017 Γ— 10⁹⁡(96-digit number)
50175196375363857632…60179698179693281279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.017 Γ— 10⁹⁡(96-digit number)
50175196375363857632…60179698179693281281
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
1.003 Γ— 10⁹⁢(97-digit number)
10035039275072771526…20359396359386562559
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
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