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Block #2,644,848

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/2/2018, 4:11:24 PM Β· Difficulty 11.7191 Β· 4,198,044 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6b0b2a4d1a2fb5e4c297f5806ac589a71dac7547fee7c73e5db217368d7145aa
View on Chainz β†—

Height

#2,644,848

Difficulty

11.719080

Transactions

1

Size

201 B

Version

2

Bits

0bb815a7

Nonce

131,182,628

Timestamp

5/2/2018, 4:11:24 PM

Confirmations

4,198,044

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

b9711959590474de8ba50667296a954d54601dd7e297b77fdebee20aed806092
Transactions (1)
Coinbaseb9711959590474…bee20aed806092
1 in β†’ 1 out7.2700 XPM110 B
Adqah8zh…1WwoHJ9t
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.

2.702 Γ— 10⁹⁷(98-digit number)
27029823314441754113…93033769846372761599
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
2.702 Γ— 10⁹⁷(98-digit number)
27029823314441754113…93033769846372761599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.702 Γ— 10⁹⁷(98-digit number)
27029823314441754113…93033769846372761601
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
5.405 Γ— 10⁹⁷(98-digit number)
54059646628883508226…86067539692745523199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.405 Γ— 10⁹⁷(98-digit number)
54059646628883508226…86067539692745523201
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
1.081 Γ— 10⁹⁸(99-digit number)
10811929325776701645…72135079385491046399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.081 Γ— 10⁹⁸(99-digit number)
10811929325776701645…72135079385491046401
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
2.162 Γ— 10⁹⁸(99-digit number)
21623858651553403290…44270158770982092799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.162 Γ— 10⁹⁸(99-digit number)
21623858651553403290…44270158770982092801
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
4.324 Γ— 10⁹⁸(99-digit number)
43247717303106806581…88540317541964185599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.324 Γ— 10⁹⁸(99-digit number)
43247717303106806581…88540317541964185601
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
8.649 Γ— 10⁹⁸(99-digit number)
86495434606213613162…77080635083928371199
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
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