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Block #842,533

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/6/2014, 5:17:11 PM Β· Difficulty 10.9736

TWN
Bi-Twin Chain

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

Block Header
Block Hash
11acad5ebae1982d865fe6b02dc1055b2cf5b2315b9d4f3d91223d32028034e0
View on Chainz β†—

Height

#842,533

Difficulty

10.973565

Transactions

Timestamp

12/6/2014, 5:17:11 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.

4.079 Γ— 10⁹²(93-digit number)
40793946137559788028…73474889722235701149
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
4.079 Γ— 10⁹²(93-digit number)
40793946137559788028…73474889722235701149
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.079 Γ— 10⁹²(93-digit number)
40793946137559788028…73474889722235701151
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
8.158 Γ— 10⁹²(93-digit number)
81587892275119576056…46949779444471402299
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.158 Γ— 10⁹²(93-digit number)
81587892275119576056…46949779444471402301
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
1.631 Γ— 10⁹³(94-digit number)
16317578455023915211…93899558888942804599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.631 Γ— 10⁹³(94-digit number)
16317578455023915211…93899558888942804601
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
3.263 Γ— 10⁹³(94-digit number)
32635156910047830422…87799117777885609199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.263 Γ— 10⁹³(94-digit number)
32635156910047830422…87799117777885609201
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
6.527 Γ— 10⁹³(94-digit number)
65270313820095660845…75598235555771218399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.527 Γ— 10⁹³(94-digit number)
65270313820095660845…75598235555771218401
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
1.305 Γ— 10⁹⁴(95-digit number)
13054062764019132169…51196471111542436799
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:β€”
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