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Block #2,636,268

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/29/2018, 12:42:38 PM Β· Difficulty 11.3721 Β· 4,197,318 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ad11c8fa7a0d62a7b363b63c83199b8e9940a87fe6f6dd4362c48a101ccaf15c
View on Chainz β†—

Height

#2,636,268

Difficulty

11.372062

Transactions

2

Size

426 B

Version

2

Bits

0b5f3f7b

Nonce

696,168,860

Timestamp

4/29/2018, 12:42:38 PM

Confirmations

4,197,318

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

9d0bce2f4052436e0d13c0ce81860abbdc2235a5204f6e02f821a785291d4a3f
Transactions (2)
Coinbased0d7d498e3ca0a…4f52263a9885fd
1 in β†’ 1 out7.7300 XPM110 B
Adqah8zh…1WwoHJ9t
7c9ac412b6e2ed…f63a38d627c7f2
1 in β†’ 2 out179905.0462 XPM226 B
AGafMD9U…qUye8cWTALMoBnaf…R3CpT5P8
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.

1.342 Γ— 10⁹⁡(96-digit number)
13422977753115791495…14769950389042641919
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
1.342 Γ— 10⁹⁡(96-digit number)
13422977753115791495…14769950389042641919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.342 Γ— 10⁹⁡(96-digit number)
13422977753115791495…14769950389042641921
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
2.684 Γ— 10⁹⁡(96-digit number)
26845955506231582990…29539900778085283839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.684 Γ— 10⁹⁡(96-digit number)
26845955506231582990…29539900778085283841
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
5.369 Γ— 10⁹⁡(96-digit number)
53691911012463165980…59079801556170567679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.369 Γ— 10⁹⁡(96-digit number)
53691911012463165980…59079801556170567681
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
1.073 Γ— 10⁹⁢(97-digit number)
10738382202492633196…18159603112341135359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.073 Γ— 10⁹⁢(97-digit number)
10738382202492633196…18159603112341135361
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
2.147 Γ— 10⁹⁢(97-digit number)
21476764404985266392…36319206224682270719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.147 Γ— 10⁹⁢(97-digit number)
21476764404985266392…36319206224682270721
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
4.295 Γ— 10⁹⁢(97-digit number)
42953528809970532784…72638412449364541439
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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