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Block #1,409,486

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/12/2016, 12:47:30 AM Β· Difficulty 10.8062 Β· 5,408,238 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ee896bee7dda7ab360fda7450e51f02d2df0869faf3fdd334f40f3c08ed69896
View on Chainz β†—

Height

#1,409,486

Difficulty

10.806161

Transactions

2

Size

572 B

Version

2

Bits

0ace6096

Nonce

1,359,769,822

Timestamp

1/12/2016, 12:47:30 AM

Confirmations

5,408,238

Mined by

⛏️ P2SHATHQc6Jfn6sm17NyBFrYpd7bdjGnPLJ663

Merkle Root

75b8b9c84ea02cfe69f452cc6cda1b6875d44280782f3a3c7e11280ebac14877
Transactions (2)
Coinbase301f412e3460af…54eed47f856ca8
1 in β†’ 1 out8.5600 XPM109 B
ATHQc6Jf…GnPLJ663
e81a21e43cabf9…c87ecec8371321
2 in β†’ 2 out147.7826 XPM373 B
AKAzpMsK…mAiHm6gKAcMpew3F…1yR4JhRa
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.

4.891 Γ— 10⁹⁴(95-digit number)
48911008472005692958…58383503707024569039
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
4.891 Γ— 10⁹⁴(95-digit number)
48911008472005692958…58383503707024569039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.891 Γ— 10⁹⁴(95-digit number)
48911008472005692958…58383503707024569041
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
9.782 Γ— 10⁹⁴(95-digit number)
97822016944011385917…16767007414049138079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.782 Γ— 10⁹⁴(95-digit number)
97822016944011385917…16767007414049138081
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
1.956 Γ— 10⁹⁡(96-digit number)
19564403388802277183…33534014828098276159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.956 Γ— 10⁹⁡(96-digit number)
19564403388802277183…33534014828098276161
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
3.912 Γ— 10⁹⁡(96-digit number)
39128806777604554367…67068029656196552319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.912 Γ— 10⁹⁡(96-digit number)
39128806777604554367…67068029656196552321
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
7.825 Γ— 10⁹⁡(96-digit number)
78257613555209108734…34136059312393104639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.825 Γ— 10⁹⁡(96-digit number)
78257613555209108734…34136059312393104641
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:57,785,851 XPMΒ·at block #6,817,723 Β· updates every 60s
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