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Block #399,568

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/11/2014, 12:16:13 PM Β· Difficulty 10.4267 Β· 6,411,146 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
79339678d14778e91b1d95d1099263052b5d408538461e33d27e7ae043bb2ae2
View on Chainz β†—

Height

#399,568

Difficulty

10.426674

Transactions

2

Size

575 B

Version

2

Bits

0a6d3a85

Nonce

10,393

Timestamp

2/11/2014, 12:16:13 PM

Confirmations

6,411,146

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

badc7b0eeb0a3e62bd90916e7c15d0ca643a3dcabb92674cde4857a449ec35f9
Transactions (2)
Coinbasea401d064f6da1a…26492ce8bd275b
1 in β†’ 1 out9.1900 XPM110 B
AeKNrjNj…1NEq95Ta
8792759ff40b26…e54a5cc4bd635d
2 in β†’ 2 out17.4097 XPM376 B
ASPN7sey…8GXwZY8RALaoweSv…Ce8SAL5a
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.

2.806 Γ— 10⁹³(94-digit number)
28069408417561627638…04507444907726601599
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
2.806 Γ— 10⁹³(94-digit number)
28069408417561627638…04507444907726601599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.806 Γ— 10⁹³(94-digit number)
28069408417561627638…04507444907726601601
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
5.613 Γ— 10⁹³(94-digit number)
56138816835123255277…09014889815453203199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.613 Γ— 10⁹³(94-digit number)
56138816835123255277…09014889815453203201
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
1.122 Γ— 10⁹⁴(95-digit number)
11227763367024651055…18029779630906406399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.122 Γ— 10⁹⁴(95-digit number)
11227763367024651055…18029779630906406401
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
2.245 Γ— 10⁹⁴(95-digit number)
22455526734049302111…36059559261812812799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.245 Γ— 10⁹⁴(95-digit number)
22455526734049302111…36059559261812812801
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
4.491 Γ— 10⁹⁴(95-digit number)
44911053468098604222…72119118523625625599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.491 Γ— 10⁹⁴(95-digit number)
44911053468098604222…72119118523625625601
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:57,729,799 XPMΒ·at block #6,810,713 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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