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Block #2,842,354

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/16/2018, 8:25:31 PM Β· Difficulty 11.7233 Β· 4,000,799 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
efd2727f16d594a49142fc0143e2d44b39792198b4aa8a5a41a87fccced32b60
View on Chainz β†—

Height

#2,842,354

Difficulty

11.723336

Transactions

1

Size

200 B

Version

2

Bits

0bb92c85

Nonce

67,171,130

Timestamp

9/16/2018, 8:25:31 PM

Confirmations

4,000,799

Mined by

⛏️ P2SHAbLsuNA1eAok2ewqoS2jVxDDg9TAPYAbdP

Merkle Root

0ec459f22356c80c53bcac07a9ca2d1adbbd3d8b783a766a5e614d7781fbbad1
Transactions (1)
Coinbase0ec459f22356c8…614d7781fbbad1
1 in β†’ 1 out7.2600 XPM110 B
AbLsuNA1…TAPYAbdP
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.

7.417 Γ— 10⁹⁴(95-digit number)
74173479762847215859…59733144058853616719
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
7.417 Γ— 10⁹⁴(95-digit number)
74173479762847215859…59733144058853616719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.417 Γ— 10⁹⁴(95-digit number)
74173479762847215859…59733144058853616721
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
1.483 Γ— 10⁹⁡(96-digit number)
14834695952569443171…19466288117707233439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.483 Γ— 10⁹⁡(96-digit number)
14834695952569443171…19466288117707233441
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
2.966 Γ— 10⁹⁡(96-digit number)
29669391905138886343…38932576235414466879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.966 Γ— 10⁹⁡(96-digit number)
29669391905138886343…38932576235414466881
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
5.933 Γ— 10⁹⁡(96-digit number)
59338783810277772687…77865152470828933759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.933 Γ— 10⁹⁡(96-digit number)
59338783810277772687…77865152470828933761
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
1.186 Γ— 10⁹⁢(97-digit number)
11867756762055554537…55730304941657867519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.186 Γ— 10⁹⁢(97-digit number)
11867756762055554537…55730304941657867521
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
2.373 Γ— 10⁹⁢(97-digit number)
23735513524111109075…11460609883315735039
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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