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Block #1,364,807

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/11/2015, 3:55:23 AM Β· Difficulty 10.8463 Β· 5,430,769 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0185a1a08d38a62bfda1fee400e42f5d58fe4ba044a07294c0cbc620dc5bb9da
View on Chainz β†—

Height

#1,364,807

Difficulty

10.846302

Transactions

2

Size

9.38 KB

Version

2

Bits

0ad8a73a

Nonce

360,515,461

Timestamp

12/11/2015, 3:55:23 AM

Confirmations

5,430,769

Mined by

⛏️ P2SHAJqPYiaGbJn5tUKKCesoVQrJd4tfQiQeyc

Merkle Root

c9479010910fe73f50213f78d7dbfc98b3df312a5da33590a34e65e15f6e3b0d
Transactions (2)
Coinbase24d4b848899b5d…fc936c7e411f57
1 in β†’ 1 out8.6900 XPM110 B
AJqPYiaG…tfQiQeyc
5385f5b91dccd3…4af0abca132edc
63 in β†’ 2 out150.3853 XPM9.18 KB
AJVeRHXf…C2yREH1fAHaA2XMK…7DLnhLvk
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.

4.333 Γ— 10⁹⁴(95-digit number)
43338402799012825997…94508830406871201819
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
4.333 Γ— 10⁹⁴(95-digit number)
43338402799012825997…94508830406871201819
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.333 Γ— 10⁹⁴(95-digit number)
43338402799012825997…94508830406871201821
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
8.667 Γ— 10⁹⁴(95-digit number)
86676805598025651994…89017660813742403639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.667 Γ— 10⁹⁴(95-digit number)
86676805598025651994…89017660813742403641
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
1.733 Γ— 10⁹⁡(96-digit number)
17335361119605130398…78035321627484807279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.733 Γ— 10⁹⁡(96-digit number)
17335361119605130398…78035321627484807281
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
3.467 Γ— 10⁹⁡(96-digit number)
34670722239210260797…56070643254969614559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.467 Γ— 10⁹⁡(96-digit number)
34670722239210260797…56070643254969614561
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
6.934 Γ— 10⁹⁡(96-digit number)
69341444478420521595…12141286509939229119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.934 Γ— 10⁹⁡(96-digit number)
69341444478420521595…12141286509939229121
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:57,608,669 XPMΒ·at block #6,795,575 Β· updates every 60s
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