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Block #1,673,282

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2016, 10:10:33 PM Β· Difficulty 10.6959 Β· 5,153,460 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4c345f3d2333397bae1e079e7246d87747846f226d0d851c33501429aa2f39b9
View on Chainz β†—

Height

#1,673,282

Difficulty

10.695929

Transactions

2

Size

460 B

Version

2

Bits

0ab22863

Nonce

1,950,708,294

Timestamp

7/14/2016, 10:10:33 PM

Confirmations

5,153,460

Mined by

⛏️ P2SHAZU7hsWUsUrQ9u6YCbpCeYBnmeZZFm35qK

Merkle Root

7f645029e837369b237420b894717dcaa206fca36d08a7eb4c7fea77f840cffb
Transactions (2)
Coinbase977407ca6f50ba…91e5555763c0fa
1 in β†’ 1 out8.7400 XPM110 B
AZU7hsWU…ZZFm35qK
37dfa0382e246f…297589284b4ccb
1 in β†’ 3 out27.3194 XPM260 B
AR6qgsuL…x1tjMz93ATBh6YHX…cVajUv2UAKsebF9o…26T4a6vn
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.

3.930 Γ— 10⁹⁴(95-digit number)
39305122208494634357…69522157990305632049
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
3.930 Γ— 10⁹⁴(95-digit number)
39305122208494634357…69522157990305632049
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.930 Γ— 10⁹⁴(95-digit number)
39305122208494634357…69522157990305632051
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
7.861 Γ— 10⁹⁴(95-digit number)
78610244416989268714…39044315980611264099
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.861 Γ— 10⁹⁴(95-digit number)
78610244416989268714…39044315980611264101
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
1.572 Γ— 10⁹⁡(96-digit number)
15722048883397853742…78088631961222528199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.572 Γ— 10⁹⁡(96-digit number)
15722048883397853742…78088631961222528201
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
3.144 Γ— 10⁹⁡(96-digit number)
31444097766795707485…56177263922445056399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.144 Γ— 10⁹⁡(96-digit number)
31444097766795707485…56177263922445056401
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
6.288 Γ— 10⁹⁡(96-digit number)
62888195533591414971…12354527844890112799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.288 Γ— 10⁹⁡(96-digit number)
62888195533591414971…12354527844890112801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.257 Γ— 10⁹⁢(97-digit number)
12577639106718282994…24709055689780225599
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,858,092 XPMΒ·at block #6,826,741 Β· updates every 60s
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