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Block #726,911

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/18/2014, 5:53:19 AM Β· Difficulty 10.9612 Β· 6,087,323 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bbfc8e7d76241bfdbce4cac181baf419965f3bf1d3011928540f0a3460dae6d2
View on Chainz β†—

Height

#726,911

Difficulty

10.961160

Transactions

2

Size

432 B

Version

2

Bits

0af60e9b

Nonce

904,233,511

Timestamp

9/18/2014, 5:53:19 AM

Confirmations

6,087,323

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

3ad92bdc0d1cc1a0a06a0ae3a4c623d9ea74e91880bf39abe9c24ac04fbf47ab
Transactions (2)
Coinbase1997683f33a3fa…728ed7dc0dcc9c
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
e59608e65c98f4…2d862425c1fc49
1 in β†’ 2 out1.0831 XPM226 B
AbEHpita…RpeBpsSeAYaJm4BX…6DqqweQv
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.

1.448 Γ— 10⁹⁡(96-digit number)
14483734028649541704…80762484474941482239
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
1.448 Γ— 10⁹⁡(96-digit number)
14483734028649541704…80762484474941482239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.448 Γ— 10⁹⁡(96-digit number)
14483734028649541704…80762484474941482241
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
2.896 Γ— 10⁹⁡(96-digit number)
28967468057299083408…61524968949882964479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.896 Γ— 10⁹⁡(96-digit number)
28967468057299083408…61524968949882964481
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
5.793 Γ— 10⁹⁡(96-digit number)
57934936114598166816…23049937899765928959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.793 Γ— 10⁹⁡(96-digit number)
57934936114598166816…23049937899765928961
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
1.158 Γ— 10⁹⁢(97-digit number)
11586987222919633363…46099875799531857919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.158 Γ— 10⁹⁢(97-digit number)
11586987222919633363…46099875799531857921
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
2.317 Γ— 10⁹⁢(97-digit number)
23173974445839266726…92199751599063715839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.317 Γ— 10⁹⁢(97-digit number)
23173974445839266726…92199751599063715841
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:57,757,943 XPMΒ·at block #6,814,233 Β· updates every 60s
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