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Block #2,021,498

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/13/2017, 5:28:46 PM Β· Difficulty 10.7124 Β· 4,820,599 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fd5c9f02779f9a156a75da7261340c51f6f179623084c4e6fca1aa0b3e6091fa
View on Chainz β†—

Height

#2,021,498

Difficulty

10.712447

Transactions

2

Size

64.47 KB

Version

2

Bits

0ab662ea

Nonce

312,245,417

Timestamp

3/13/2017, 5:28:46 PM

Confirmations

4,820,599

Mined by

⛏️ P2SHAeT1pzasDJb2EJ22QHCwP6yQsHTqcTnr4a

Merkle Root

df2afb5f4eb90adefb1a590cad4b437751e5a70e251fca6766b64fc94120e0c6
Transactions (2)
Coinbase02805ea6a5df2d…41fc739d8e395b
1 in β†’ 1 out9.3700 XPM109 B
AeT1pzas…TqcTnr4a
e36ae15624c55b…55bc5c7f284186
577 in β†’ 1 out5000.0000 XPM64.27 KB
ARdVe6hk…QmgEA7NV
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.

2.618 Γ— 10⁹⁴(95-digit number)
26182269847661757316…84157161567061725919
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
2.618 Γ— 10⁹⁴(95-digit number)
26182269847661757316…84157161567061725919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.618 Γ— 10⁹⁴(95-digit number)
26182269847661757316…84157161567061725921
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
5.236 Γ— 10⁹⁴(95-digit number)
52364539695323514633…68314323134123451839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.236 Γ— 10⁹⁴(95-digit number)
52364539695323514633…68314323134123451841
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
1.047 Γ— 10⁹⁡(96-digit number)
10472907939064702926…36628646268246903679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.047 Γ— 10⁹⁡(96-digit number)
10472907939064702926…36628646268246903681
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
2.094 Γ— 10⁹⁡(96-digit number)
20945815878129405853…73257292536493807359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.094 Γ— 10⁹⁡(96-digit number)
20945815878129405853…73257292536493807361
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
4.189 Γ— 10⁹⁡(96-digit number)
41891631756258811707…46514585072987614719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.189 Γ— 10⁹⁡(96-digit number)
41891631756258811707…46514585072987614721
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:57,981,162 XPMΒ·at block #6,842,096 Β· updates every 60s
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