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Block #842,443

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/6/2014, 3:39:01 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
8115aa03cbe34db174d217a9852239963a931409f3a4a730d4457be68b46262e
View on Chainz β†—

Height

#842,443

Difficulty

10.973607

Transactions

Timestamp

12/6/2014, 3:39:01 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.

7.493 Γ— 10⁹⁢(97-digit number)
74936044162923139661…66461814679147069439
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
7.493 Γ— 10⁹⁢(97-digit number)
74936044162923139661…66461814679147069439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.493 Γ— 10⁹⁢(97-digit number)
74936044162923139661…66461814679147069441
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
1.498 Γ— 10⁹⁷(98-digit number)
14987208832584627932…32923629358294138879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.498 Γ— 10⁹⁷(98-digit number)
14987208832584627932…32923629358294138881
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
2.997 Γ— 10⁹⁷(98-digit number)
29974417665169255864…65847258716588277759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.997 Γ— 10⁹⁷(98-digit number)
29974417665169255864…65847258716588277761
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
5.994 Γ— 10⁹⁷(98-digit number)
59948835330338511729…31694517433176555519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.994 Γ— 10⁹⁷(98-digit number)
59948835330338511729…31694517433176555521
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
1.198 Γ— 10⁹⁸(99-digit number)
11989767066067702345…63389034866353111039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.198 Γ— 10⁹⁸(99-digit number)
11989767066067702345…63389034866353111041
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
2.397 Γ— 10⁹⁸(99-digit number)
23979534132135404691…26778069732706222079
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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