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Block #2,808,109

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/24/2018, 3:21:23 PM Β· Difficulty 11.6734

TWN
Bi-Twin Chain

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

Block Header
Block Hash
734345c4793c41614c927b9752df5bf9ab87e1ed34b81bad3aa4f0eb9e9f2585
View on Chainz β†—

Height

#2,808,109

Difficulty

11.673368

Transactions

Timestamp

8/24/2018, 3:21:23 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.

1.958 Γ— 10⁹⁷(98-digit number)
19586271031565968088…31614329029669683199
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
1.958 Γ— 10⁹⁷(98-digit number)
19586271031565968088…31614329029669683199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.958 Γ— 10⁹⁷(98-digit number)
19586271031565968088…31614329029669683201
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
3.917 Γ— 10⁹⁷(98-digit number)
39172542063131936177…63228658059339366399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.917 Γ— 10⁹⁷(98-digit number)
39172542063131936177…63228658059339366401
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
7.834 Γ— 10⁹⁷(98-digit number)
78345084126263872355…26457316118678732799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.834 Γ— 10⁹⁷(98-digit number)
78345084126263872355…26457316118678732801
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
1.566 Γ— 10⁹⁸(99-digit number)
15669016825252774471…52914632237357465599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.566 Γ— 10⁹⁸(99-digit number)
15669016825252774471…52914632237357465601
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
3.133 Γ— 10⁹⁸(99-digit number)
31338033650505548942…05829264474714931199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.133 Γ— 10⁹⁸(99-digit number)
31338033650505548942…05829264474714931201
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
6.267 Γ— 10⁹⁸(99-digit number)
62676067301011097884…11658528949429862399
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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