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Block #1,765,920

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/16/2016, 4:38:38 PM Β· Difficulty 10.7440 Β· 5,076,869 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9e0ae5ac83d8ccb8b3896d842b48c446be6e540eb8e9e27c7f14825cbccc3d6b
View on Chainz β†—

Height

#1,765,920

Difficulty

10.743964

Transactions

2

Size

426 B

Version

2

Bits

0abe746f

Nonce

1,002,981,245

Timestamp

9/16/2016, 4:38:38 PM

Confirmations

5,076,869

Mined by

⛏️ P2SHAQKjBojtnGhZkjXmyP5vqEcSRT1GXUt98V

Merkle Root

23e07ce7810c33d6380a9655264604d1f1bad69d8d42038bde4623ada3f86f0a
Transactions (2)
Coinbase3589ca6f2d1c9c…bc71c0efe1190f
1 in β†’ 1 out8.6600 XPM109 B
AQKjBojt…1GXUt98V
458ada6223da0f…99b552cbc6c9dc
1 in β†’ 2 out0.0731 XPM226 B
AVEtdVEg…C8kuubTdAaDo5YY5…3bPoj1WA
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.

4.128 Γ— 10⁹⁢(97-digit number)
41280812091721990499…41630556526400220159
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
4.128 Γ— 10⁹⁢(97-digit number)
41280812091721990499…41630556526400220159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.128 Γ— 10⁹⁢(97-digit number)
41280812091721990499…41630556526400220161
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
8.256 Γ— 10⁹⁢(97-digit number)
82561624183443980999…83261113052800440319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.256 Γ— 10⁹⁢(97-digit number)
82561624183443980999…83261113052800440321
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
1.651 Γ— 10⁹⁷(98-digit number)
16512324836688796199…66522226105600880639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.651 Γ— 10⁹⁷(98-digit number)
16512324836688796199…66522226105600880641
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
3.302 Γ— 10⁹⁷(98-digit number)
33024649673377592399…33044452211201761279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.302 Γ— 10⁹⁷(98-digit number)
33024649673377592399…33044452211201761281
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
6.604 Γ— 10⁹⁷(98-digit number)
66049299346755184799…66088904422403522559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.604 Γ— 10⁹⁷(98-digit number)
66049299346755184799…66088904422403522561
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:57,986,650 XPMΒ·at block #6,842,788 Β· updates every 60s
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