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Block #858,344

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/18/2014, 1:02:11 PM Β· Difficulty 10.9669 Β· 5,985,558 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5f23143dad3dc0582c7dea16fba491fb800ab3355ee993b61863bf0c4ba8095f
View on Chainz β†—

Height

#858,344

Difficulty

10.966915

Transactions

2

Size

6.52 KB

Version

2

Bits

0af787b9

Nonce

295,088,270

Timestamp

12/18/2014, 1:02:11 PM

Confirmations

5,985,558

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

34334387e0440afe4c104b6ffb64783a3282da3f326f2e9e614928fcac5ee0b9
Transactions (2)
Coinbaseac276515eb96e5…d1a2cd5bdd25ab
1 in β†’ 1 out8.4100 XPM116 B
ANSXnLY2…Sd25TjkD
6e07fc7bbf4c14…e73624b4310d26
43 in β†’ 3 out19.2455 XPM6.32 KB
AQdVNfKp…C6YPKeLtAbecWDS9…1vtToSMLAYeGLxtJ…3XFCDFMm
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.

3.308 Γ— 10⁹⁴(95-digit number)
33084872600130453301…96847141282906644799
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
3.308 Γ— 10⁹⁴(95-digit number)
33084872600130453301…96847141282906644799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.308 Γ— 10⁹⁴(95-digit number)
33084872600130453301…96847141282906644801
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
6.616 Γ— 10⁹⁴(95-digit number)
66169745200260906603…93694282565813289599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.616 Γ— 10⁹⁴(95-digit number)
66169745200260906603…93694282565813289601
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
1.323 Γ— 10⁹⁡(96-digit number)
13233949040052181320…87388565131626579199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.323 Γ— 10⁹⁡(96-digit number)
13233949040052181320…87388565131626579201
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
2.646 Γ— 10⁹⁡(96-digit number)
26467898080104362641…74777130263253158399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.646 Γ— 10⁹⁡(96-digit number)
26467898080104362641…74777130263253158401
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
5.293 Γ— 10⁹⁡(96-digit number)
52935796160208725282…49554260526506316799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.293 Γ— 10⁹⁡(96-digit number)
52935796160208725282…49554260526506316801
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:57,995,587 XPMΒ·at block #6,843,901 Β· updates every 60s
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