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Block #3,304,133

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/10/2019, 2:08:54 AM Β· Difficulty 11.0007 Β· 3,538,791 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d3d8e5d6deec3207685ad3bd4912aa4aff59d44839d42f115fc194b67210fc18
View on Chainz β†—

Height

#3,304,133

Difficulty

11.000721

Transactions

2

Size

1018 B

Version

2

Bits

0b002f3c

Nonce

275,096,811

Timestamp

8/10/2019, 2:08:54 AM

Confirmations

3,538,791

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

154453a2d92ae74e790a5a00ed858cb2f10612c593304ad6bdae9f3a4c2ab14e
Transactions (2)
Coinbase35a0048ab56571…2feee0aa2b005f
1 in β†’ 1 out8.2600 XPM110 B
ASiq2qtK…VMhmk7yL
062dfed305d372…0a718d8b85ac9a
5 in β†’ 2 out948.8438 XPM818 B
AGgNMpq4…MY7RLwLHAek7oPfd…55Lx6rVv
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.

9.012 Γ— 10⁹⁴(95-digit number)
90127069049408519781…89307578277851776199
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
9.012 Γ— 10⁹⁴(95-digit number)
90127069049408519781…89307578277851776199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.012 Γ— 10⁹⁴(95-digit number)
90127069049408519781…89307578277851776201
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
1.802 Γ— 10⁹⁡(96-digit number)
18025413809881703956…78615156555703552399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.802 Γ— 10⁹⁡(96-digit number)
18025413809881703956…78615156555703552401
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
3.605 Γ— 10⁹⁡(96-digit number)
36050827619763407912…57230313111407104799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.605 Γ— 10⁹⁡(96-digit number)
36050827619763407912…57230313111407104801
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
7.210 Γ— 10⁹⁡(96-digit number)
72101655239526815825…14460626222814209599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.210 Γ— 10⁹⁡(96-digit number)
72101655239526815825…14460626222814209601
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
1.442 Γ— 10⁹⁢(97-digit number)
14420331047905363165…28921252445628419199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.442 Γ— 10⁹⁢(97-digit number)
14420331047905363165…28921252445628419201
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
2.884 Γ— 10⁹⁢(97-digit number)
28840662095810726330…57842504891256838399
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:57,987,740 XPMΒ·at block #6,842,923 Β· updates every 60s
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