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Block #1,344,522

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/27/2015, 4:49:43 PM Β· Difficulty 10.8153

TWN
Bi-Twin Chain

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

Block Header
Block Hash
06049ce785475d604ec8480e86b7dcbc4b03c6b91cdb5ff25ecb97867eb4626a
View on Chainz β†—

Height

#1,344,522

Difficulty

10.815296

Transactions

Timestamp

11/27/2015, 4:49:43 PM

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.

1.758 Γ— 10⁹²(93-digit number)
17588373213195681280…03059043193142976259
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
1.758 Γ— 10⁹²(93-digit number)
17588373213195681280…03059043193142976259
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.758 Γ— 10⁹²(93-digit number)
17588373213195681280…03059043193142976261
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
3.517 Γ— 10⁹²(93-digit number)
35176746426391362561…06118086386285952519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.517 Γ— 10⁹²(93-digit number)
35176746426391362561…06118086386285952521
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
7.035 Γ— 10⁹²(93-digit number)
70353492852782725122…12236172772571905039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.035 Γ— 10⁹²(93-digit number)
70353492852782725122…12236172772571905041
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
1.407 Γ— 10⁹³(94-digit number)
14070698570556545024…24472345545143810079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.407 Γ— 10⁹³(94-digit number)
14070698570556545024…24472345545143810081
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
2.814 Γ— 10⁹³(94-digit number)
28141397141113090048…48944691090287620159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.814 Γ— 10⁹³(94-digit number)
28141397141113090048…48944691090287620161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:β€”
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