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Block #2,583,314

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 3/24/2018, 5:27:49 PM Β· Difficulty 11.1688 Β· 4,257,098 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
599d8aa1432bc8f852be0a069f54aba029531cec89d6bd481ca88288fbcf8a5d
View on Chainz β†—

Height

#2,583,314

Difficulty

11.168790

Transactions

2

Size

9.38 KB

Version

2

Bits

0b2b35cb

Nonce

142,578,069

Timestamp

3/24/2018, 5:27:49 PM

Confirmations

4,257,098

Mined by

⛏️ P2SHAPQM2pmKmw5qinznBRUnczg5mMnUQj4Wbi

Merkle Root

03dc1fae5e3edc1ea5233fd3d36b2ed7969283ec138a6610817e22a2f1958b87
Transactions (2)
Coinbase54d8d71a41e461…74d03a9172f707
1 in β†’ 1 out8.1000 XPM110 B
APQM2pmK…nUQj4Wbi
54c8cedb00a2c8…75400bb1fe3c51
63 in β†’ 2 out260.9044 XPM9.19 KB
AGW8iVgz…xMg7SUHXAUFiMnR5…DW9ow5zp
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.

1.484 Γ— 10⁹⁷(98-digit number)
14840691229062822853…90124552158144255999
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
1.484 Γ— 10⁹⁷(98-digit number)
14840691229062822853…90124552158144255999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.484 Γ— 10⁹⁷(98-digit number)
14840691229062822853…90124552158144256001
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
2.968 Γ— 10⁹⁷(98-digit number)
29681382458125645706…80249104316288511999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.968 Γ— 10⁹⁷(98-digit number)
29681382458125645706…80249104316288512001
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
5.936 Γ— 10⁹⁷(98-digit number)
59362764916251291412…60498208632577023999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.936 Γ— 10⁹⁷(98-digit number)
59362764916251291412…60498208632577024001
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
1.187 Γ— 10⁹⁸(99-digit number)
11872552983250258282…20996417265154047999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.187 Γ— 10⁹⁸(99-digit number)
11872552983250258282…20996417265154048001
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
2.374 Γ— 10⁹⁸(99-digit number)
23745105966500516565…41992834530308095999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.374 Γ— 10⁹⁸(99-digit number)
23745105966500516565…41992834530308096001
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
4.749 Γ— 10⁹⁸(99-digit number)
47490211933001033130…83985669060616191999
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
4.749 Γ— 10⁹⁸(99-digit number)
47490211933001033130…83985669060616192001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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
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