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Block #2,649,289

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/5/2018, 3:16:20 AM Β· Difficulty 11.7650 Β· 4,188,358 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e4b32e7ac95332e34af1f0d7d951a75be8c9cfefeac5fd5e228900eecbe2c422
View on Chainz β†—

Height

#2,649,289

Difficulty

11.764997

Transactions

2

Size

426 B

Version

2

Bits

0bc3d6dd

Nonce

1,900,904,100

Timestamp

5/5/2018, 3:16:20 AM

Confirmations

4,188,358

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

b68ea085fd3805270dd5ef4d9616b445f6a6e5cb1b0589736df025e9c6cf3154
Transactions (2)
Coinbasec072cfaeb1eca2…d1a752a242e927
1 in β†’ 1 out7.2200 XPM110 B
Adqah8zh…1WwoHJ9t
0a2bb609368f28…f8b159c6fdec11
1 in β†’ 2 out1.6059 XPM226 B
AYroGxNw…U9nNJQKRAY5Sm3EA…SyjtRQ5W
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.

2.817 Γ— 10⁹⁡(96-digit number)
28173931972828594121…80130559134913557119
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
2.817 Γ— 10⁹⁡(96-digit number)
28173931972828594121…80130559134913557119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.817 Γ— 10⁹⁡(96-digit number)
28173931972828594121…80130559134913557121
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
5.634 Γ— 10⁹⁡(96-digit number)
56347863945657188243…60261118269827114239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.634 Γ— 10⁹⁡(96-digit number)
56347863945657188243…60261118269827114241
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
1.126 Γ— 10⁹⁢(97-digit number)
11269572789131437648…20522236539654228479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.126 Γ— 10⁹⁢(97-digit number)
11269572789131437648…20522236539654228481
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
2.253 Γ— 10⁹⁢(97-digit number)
22539145578262875297…41044473079308456959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.253 Γ— 10⁹⁢(97-digit number)
22539145578262875297…41044473079308456961
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
4.507 Γ— 10⁹⁢(97-digit number)
45078291156525750594…82088946158616913919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.507 Γ— 10⁹⁢(97-digit number)
45078291156525750594…82088946158616913921
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
9.015 Γ— 10⁹⁢(97-digit number)
90156582313051501189…64177892317233827839
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:57,945,503 XPMΒ·at block #6,837,646 Β· updates every 60s
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