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Block #2,644,115

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/2/2018, 8:51:05 AM Β· Difficulty 11.7023 Β· 4,194,506 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6837521f0bbb84a9313bb7221ced0ad5525c4215a31be57f6128b2e05e019150
View on Chainz β†—

Height

#2,644,115

Difficulty

11.702299

Transactions

1

Size

200 B

Version

2

Bits

0bb3c9e3

Nonce

920,072,247

Timestamp

5/2/2018, 8:51:05 AM

Confirmations

4,194,506

Mined by

⛏️ P2SHAQEkNd7rN2pyHffDJmeV1vxJiFLSxDzy2C

Merkle Root

bc1b217c4d7437012c97d0bf183dc697e6e8dac010a446e6e711a24979b23383
Transactions (1)
Coinbasebc1b217c4d7437…11a24979b23383
1 in β†’ 1 out7.2900 XPM110 B
AQEkNd7r…LSxDzy2C
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.

4.156 Γ— 10⁹⁡(96-digit number)
41563337158021639444…98745547364253808639
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
4.156 Γ— 10⁹⁡(96-digit number)
41563337158021639444…98745547364253808639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.156 Γ— 10⁹⁡(96-digit number)
41563337158021639444…98745547364253808641
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
8.312 Γ— 10⁹⁡(96-digit number)
83126674316043278888…97491094728507617279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.312 Γ— 10⁹⁡(96-digit number)
83126674316043278888…97491094728507617281
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
1.662 Γ— 10⁹⁢(97-digit number)
16625334863208655777…94982189457015234559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.662 Γ— 10⁹⁢(97-digit number)
16625334863208655777…94982189457015234561
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
3.325 Γ— 10⁹⁢(97-digit number)
33250669726417311555…89964378914030469119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.325 Γ— 10⁹⁢(97-digit number)
33250669726417311555…89964378914030469121
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
6.650 Γ— 10⁹⁢(97-digit number)
66501339452834623111…79928757828060938239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.650 Γ— 10⁹⁢(97-digit number)
66501339452834623111…79928757828060938241
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
1.330 Γ— 10⁹⁷(98-digit number)
13300267890566924622…59857515656121876479
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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