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Block #1,349,576

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/1/2015, 8:05:22 AM Β· Difficulty 10.8087 Β· 5,492,555 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b4d40e001d1ffa365b4316558cd886f0f4db8a7ce2d9f0d0d40317f5fb4b7a12
View on Chainz β†—

Height

#1,349,576

Difficulty

10.808747

Transactions

2

Size

26.13 KB

Version

2

Bits

0acf0a09

Nonce

484,925,292

Timestamp

12/1/2015, 8:05:22 AM

Confirmations

5,492,555

Mined by

⛏️ P2SHAYXiUjHGkyYCMTNGDLheAZCCmEa8TNmEdD

Merkle Root

659056f5be75cdacdbed3e21ee56f1f88d71ea923bf6770c51cafcc0c593ab92
Transactions (2)
Coinbaseabb27c0f28bd0d…b5880576ab9cbb
1 in β†’ 1 out8.8400 XPM110 B
AYXiUjHG…a8TNmEdD
86cd13fea89806…3303c2f3a46b36
179 in β†’ 2 out1034.1769 XPM25.94 KB
AJNW8vYc…vadX8gknAVpJbiVd…f3No8Y5f
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.

9.143 Γ— 10⁹³(94-digit number)
91431805127123503079…21685992156905568329
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
9.143 Γ— 10⁹³(94-digit number)
91431805127123503079…21685992156905568329
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.143 Γ— 10⁹³(94-digit number)
91431805127123503079…21685992156905568331
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
1.828 Γ— 10⁹⁴(95-digit number)
18286361025424700615…43371984313811136659
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.828 Γ— 10⁹⁴(95-digit number)
18286361025424700615…43371984313811136661
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
3.657 Γ— 10⁹⁴(95-digit number)
36572722050849401231…86743968627622273319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.657 Γ— 10⁹⁴(95-digit number)
36572722050849401231…86743968627622273321
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
7.314 Γ— 10⁹⁴(95-digit number)
73145444101698802463…73487937255244546639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.314 Γ— 10⁹⁴(95-digit number)
73145444101698802463…73487937255244546641
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
1.462 Γ— 10⁹⁡(96-digit number)
14629088820339760492…46975874510489093279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.462 Γ— 10⁹⁡(96-digit number)
14629088820339760492…46975874510489093281
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
2.925 Γ— 10⁹⁡(96-digit number)
29258177640679520985…93951749020978186559
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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