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Block #2,643,382

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/2/2018, 2:17:32 AM Β· Difficulty 11.6815

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b4b003f7a64d32681ea0012d25af8e8f6c1452b98694f434a78fdb557591c71f
View on Chainz β†—

Height

#2,643,382

Difficulty

11.681495

Transactions

Timestamp

5/2/2018, 2:17:32 AM

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.

2.740 Γ— 10⁹⁷(98-digit number)
27400325624584105527…72028007378726911999
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
2.740 Γ— 10⁹⁷(98-digit number)
27400325624584105527…72028007378726911999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.740 Γ— 10⁹⁷(98-digit number)
27400325624584105527…72028007378726912001
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
5.480 Γ— 10⁹⁷(98-digit number)
54800651249168211055…44056014757453823999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.480 Γ— 10⁹⁷(98-digit number)
54800651249168211055…44056014757453824001
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
1.096 Γ— 10⁹⁸(99-digit number)
10960130249833642211…88112029514907647999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.096 Γ— 10⁹⁸(99-digit number)
10960130249833642211…88112029514907648001
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
2.192 Γ— 10⁹⁸(99-digit number)
21920260499667284422…76224059029815295999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.192 Γ— 10⁹⁸(99-digit number)
21920260499667284422…76224059029815296001
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
4.384 Γ— 10⁹⁸(99-digit number)
43840520999334568844…52448118059630591999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.384 Γ— 10⁹⁸(99-digit number)
43840520999334568844…52448118059630592001
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
8.768 Γ— 10⁹⁸(99-digit number)
87681041998669137688…04896236119261183999
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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