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Block #395,272

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/8/2014, 2:28:37 PM Β· Difficulty 10.4126 Β· 6,413,111 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
30aac43f310d6c8d8d9ec9c4d90cc75b88490c34d3992510f51b04a8fa5a730f
View on Chainz β†—

Height

#395,272

Difficulty

10.412619

Transactions

4

Size

35.08 KB

Version

2

Bits

0a69a16b

Nonce

18,366

Timestamp

2/8/2014, 2:28:37 PM

Confirmations

6,413,111

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

27f400c6e2faab6666540cae25f414d98fcc6917427f14be6564162c7f94130f
Transactions (4)
Coinbase07fcc1d1a5a5b2…7654684574a167
1 in β†’ 1 out9.5904 XPM110 B
AeKNrjNj…1NEq95Ta
0c0eb848ca297f…4638ea39db1afc
1 in β†’ 1 out0.9900 XPM192 B
AaEfXPg2…k8UxQ7ar
26d673816e68a6…2c811970705ada
237 in β†’ 2 out248.4271 XPM34.33 KB
AYucrzW5…jcFH2zLJAV14vbFG…a1ih57x4
15844f54ad8b23…9ef430d37dd80f
2 in β†’ 2 out19.3700 XPM376 B
ALcBy7MP…nzj2PRxtAL4YBCF1…7qA1DZww
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.

1.159 Γ— 10⁹⁡(96-digit number)
11596903400285727986…73130821970893551359
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
1.159 Γ— 10⁹⁡(96-digit number)
11596903400285727986…73130821970893551359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.159 Γ— 10⁹⁡(96-digit number)
11596903400285727986…73130821970893551361
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
2.319 Γ— 10⁹⁡(96-digit number)
23193806800571455972…46261643941787102719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.319 Γ— 10⁹⁡(96-digit number)
23193806800571455972…46261643941787102721
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
4.638 Γ— 10⁹⁡(96-digit number)
46387613601142911945…92523287883574205439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.638 Γ— 10⁹⁡(96-digit number)
46387613601142911945…92523287883574205441
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
9.277 Γ— 10⁹⁡(96-digit number)
92775227202285823891…85046575767148410879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.277 Γ— 10⁹⁡(96-digit number)
92775227202285823891…85046575767148410881
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
1.855 Γ— 10⁹⁢(97-digit number)
18555045440457164778…70093151534296821759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.855 Γ— 10⁹⁢(97-digit number)
18555045440457164778…70093151534296821761
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:57,711,118 XPMΒ·at block #6,808,382 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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