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Block #2,682,934

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/29/2018, 11:17:12 AM Β· Difficulty 11.6912 Β· 4,158,530 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
49f73d17a4fac3529d4649307b7f04ea4e74cd564237b4fe66abac409033cbee
View on Chainz β†—

Height

#2,682,934

Difficulty

11.691160

Transactions

2

Size

11.69 KB

Version

2

Bits

0bb0efe1

Nonce

480,759,894

Timestamp

5/29/2018, 11:17:12 AM

Confirmations

4,158,530

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

0d3042eae0688c0d87902608241d80099eb3ad26a4ae72b372535eda4a6feb6b
Transactions (2)
Coinbase30fc4a3a0ae900…b12b1c2e4501b7
1 in β†’ 1 out7.4200 XPM110 B
Adqah8zh…1WwoHJ9t
e320a82bbb4ee0…2f8deb05e48c15
79 in β†’ 2 out631.0185 XPM11.49 KB
AdUbFbQ9…MXLm2P1GAWqwZUj6…npkqMnnb
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.

3.565 Γ— 10⁹⁡(96-digit number)
35653540967862409828…17701382949674565119
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
3.565 Γ— 10⁹⁡(96-digit number)
35653540967862409828…17701382949674565119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.565 Γ— 10⁹⁡(96-digit number)
35653540967862409828…17701382949674565121
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
7.130 Γ— 10⁹⁡(96-digit number)
71307081935724819657…35402765899349130239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.130 Γ— 10⁹⁡(96-digit number)
71307081935724819657…35402765899349130241
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
1.426 Γ— 10⁹⁢(97-digit number)
14261416387144963931…70805531798698260479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.426 Γ— 10⁹⁢(97-digit number)
14261416387144963931…70805531798698260481
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
2.852 Γ— 10⁹⁢(97-digit number)
28522832774289927863…41611063597396520959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.852 Γ— 10⁹⁢(97-digit number)
28522832774289927863…41611063597396520961
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
5.704 Γ— 10⁹⁢(97-digit number)
57045665548579855726…83222127194793041919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.704 Γ— 10⁹⁢(97-digit number)
57045665548579855726…83222127194793041921
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
1.140 Γ— 10⁹⁷(98-digit number)
11409133109715971145…66444254389586083839
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
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