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Block #2,250,934

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/14/2017, 8:50:07 AM Β· Difficulty 10.9482 Β· 4,591,124 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3fa33169aeeadf0cc49232cfd8b6758903f9b4b2148975874c42b88730247d90
View on Chainz β†—

Height

#2,250,934

Difficulty

10.948151

Transactions

2

Size

428 B

Version

2

Bits

0af2b9ff

Nonce

2,077,015,387

Timestamp

8/14/2017, 8:50:07 AM

Confirmations

4,591,124

Mined by

⛏️ P2SHAQfP2cUsASpuqikzCbcNzaCw21QMaSPjg2

Merkle Root

2725419a062654e3a392bf69e526554bde1406fb3915a15a680ed94e73efa85b
Transactions (2)
Coinbasee2d6cb5001d519…10f0d0106fe615
1 in β†’ 1 out8.3400 XPM110 B
AQfP2cUs…QMaSPjg2
174006ba28af7d…837cdb37559179
1 in β†’ 2 out1198.2675 XPM227 B
AGM7kn12…4FthXBECAN8ChhTf…8rbdSVLi
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.

4.757 Γ— 10⁹⁢(97-digit number)
47570157200807900013…06874079489169264639
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
4.757 Γ— 10⁹⁢(97-digit number)
47570157200807900013…06874079489169264639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.757 Γ— 10⁹⁢(97-digit number)
47570157200807900013…06874079489169264641
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
9.514 Γ— 10⁹⁢(97-digit number)
95140314401615800026…13748158978338529279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.514 Γ— 10⁹⁢(97-digit number)
95140314401615800026…13748158978338529281
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
1.902 Γ— 10⁹⁷(98-digit number)
19028062880323160005…27496317956677058559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.902 Γ— 10⁹⁷(98-digit number)
19028062880323160005…27496317956677058561
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
3.805 Γ— 10⁹⁷(98-digit number)
38056125760646320010…54992635913354117119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.805 Γ— 10⁹⁷(98-digit number)
38056125760646320010…54992635913354117121
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
7.611 Γ— 10⁹⁷(98-digit number)
76112251521292640020…09985271826708234239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.611 Γ— 10⁹⁷(98-digit number)
76112251521292640020…09985271826708234241
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:57,980,846 XPMΒ·at block #6,842,057 Β· updates every 60s
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