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Block #3,186,342

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/17/2019, 6:50:46 PM Β· Difficulty 11.2422 Β· 3,658,275 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e2c88bd178db63a774997487a4d2126149ddd45c7187057549bfeb0dac563c3c
View on Chainz β†—

Height

#3,186,342

Difficulty

11.242173

Transactions

1

Size

200 B

Version

2

Bits

0b3dff0b

Nonce

576,342,535

Timestamp

5/17/2019, 6:50:46 PM

Confirmations

3,658,275

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

d36771335ad5c42eed3bafae1a1b4140890f85117a1b40988caf6dfdb24c13e8
Transactions (1)
Coinbased36771335ad5c4…af6dfdb24c13e8
1 in β†’ 1 out7.9000 XPM109 B
AUMQRepm…tAfKmdW1
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.

4.289 Γ— 10⁹⁢(97-digit number)
42893743848802926755…41331975265628979199
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
4.289 Γ— 10⁹⁢(97-digit number)
42893743848802926755…41331975265628979199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.289 Γ— 10⁹⁢(97-digit number)
42893743848802926755…41331975265628979201
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
8.578 Γ— 10⁹⁢(97-digit number)
85787487697605853511…82663950531257958399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.578 Γ— 10⁹⁢(97-digit number)
85787487697605853511…82663950531257958401
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
1.715 Γ— 10⁹⁷(98-digit number)
17157497539521170702…65327901062515916799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.715 Γ— 10⁹⁷(98-digit number)
17157497539521170702…65327901062515916801
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
3.431 Γ— 10⁹⁷(98-digit number)
34314995079042341404…30655802125031833599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.431 Γ— 10⁹⁷(98-digit number)
34314995079042341404…30655802125031833601
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
6.862 Γ— 10⁹⁷(98-digit number)
68629990158084682809…61311604250063667199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.862 Γ— 10⁹⁷(98-digit number)
68629990158084682809…61311604250063667201
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
1.372 Γ— 10⁹⁸(99-digit number)
13725998031616936561…22623208500127334399
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:58,001,339 XPMΒ·at block #6,844,616 Β· updates every 60s
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