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Block #3,049,594

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/12/2019, 9:51:07 AM Β· Difficulty 10.9961 Β· 3,794,160 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
89ca75add094d493158599be4a1eb2c4bfe755f75c2191db1ccc69541f6087d0
View on Chainz β†—

Height

#3,049,594

Difficulty

10.996089

Transactions

2

Size

1.29 KB

Version

2

Bits

0afeffb2

Nonce

1,569,859,968

Timestamp

2/12/2019, 9:51:07 AM

Confirmations

3,794,160

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

fcc439fae6c17575bf8d036c6166df615b4dfb4c1cc295110d7257be3ea96bad
Transactions (2)
Coinbase3fe5354a641f3a…f45bb35c5b275d
1 in β†’ 1 out8.2800 XPM110 B
AbXwmGxD…4XXYP765
016ff26af8fc9d…8fe2ff8ccd0c62
7 in β†’ 2 out139.8641 XPM1.09 KB
AJDJNneS…5UrMWWPuAWGGfF3Z…7bFq9KQh
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.

2.215 Γ— 10⁹⁷(98-digit number)
22150179862484391207…63991889524953292799
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
2.215 Γ— 10⁹⁷(98-digit number)
22150179862484391207…63991889524953292799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.215 Γ— 10⁹⁷(98-digit number)
22150179862484391207…63991889524953292801
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
4.430 Γ— 10⁹⁷(98-digit number)
44300359724968782415…27983779049906585599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.430 Γ— 10⁹⁷(98-digit number)
44300359724968782415…27983779049906585601
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
8.860 Γ— 10⁹⁷(98-digit number)
88600719449937564830…55967558099813171199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.860 Γ— 10⁹⁷(98-digit number)
88600719449937564830…55967558099813171201
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
1.772 Γ— 10⁹⁸(99-digit number)
17720143889987512966…11935116199626342399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.772 Γ— 10⁹⁸(99-digit number)
17720143889987512966…11935116199626342401
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
3.544 Γ— 10⁹⁸(99-digit number)
35440287779975025932…23870232399252684799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.544 Γ— 10⁹⁸(99-digit number)
35440287779975025932…23870232399252684801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,994,403 XPMΒ·at block #6,843,753 Β· updates every 60s
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