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Block #3,082,328

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/7/2019, 10:15:47 AM Β· Difficulty 11.0216 Β· 3,754,714 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a8272253d459fafe5464e97da5f7a4883a3fde4faf6db362dbe8a55815918639
View on Chainz β†—

Height

#3,082,328

Difficulty

11.021578

Transactions

2

Size

1.14 KB

Version

2

Bits

0b058625

Nonce

269,641,239

Timestamp

3/7/2019, 10:15:47 AM

Confirmations

3,754,714

Mined by

⛏️ jAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

f193a9cd02120858c7606c12ce83c0982e403950cf2be3a19384d43fb9a3b900
Transactions (2)
Coinbasefc52acb337f983…255affd3ebd23d
1 in β†’ 1 out8.2400 XPM110 B
AUhjokok…k5m93PZR
9eff9b35a0f974…79595638a10971
6 in β†’ 2 out1069.3171 XPM967 B
AZQgL5kt…6NE43uZsAHgwGWSe…DFXcbtYB
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.

5.984 Γ— 10⁹⁴(95-digit number)
59849301268817978973…10203567239429598799
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
5.984 Γ— 10⁹⁴(95-digit number)
59849301268817978973…10203567239429598799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.984 Γ— 10⁹⁴(95-digit number)
59849301268817978973…10203567239429598801
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
1.196 Γ— 10⁹⁡(96-digit number)
11969860253763595794…20407134478859197599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.196 Γ— 10⁹⁡(96-digit number)
11969860253763595794…20407134478859197601
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
2.393 Γ— 10⁹⁡(96-digit number)
23939720507527191589…40814268957718395199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.393 Γ— 10⁹⁡(96-digit number)
23939720507527191589…40814268957718395201
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
4.787 Γ— 10⁹⁡(96-digit number)
47879441015054383178…81628537915436790399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.787 Γ— 10⁹⁡(96-digit number)
47879441015054383178…81628537915436790401
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
9.575 Γ— 10⁹⁡(96-digit number)
95758882030108766357…63257075830873580799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.575 Γ— 10⁹⁡(96-digit number)
95758882030108766357…63257075830873580801
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
1.915 Γ— 10⁹⁢(97-digit number)
19151776406021753271…26514151661747161599
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:57,940,638 XPMΒ·at block #6,837,041 Β· updates every 60s
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