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Block #2,290,096

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/10/2017, 2:51:54 AM Β· Difficulty 10.9555 Β· 4,543,758 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
97c0acbdb7aadb3bdb03c9faf5f71fba8dc5ed5b2e9fcab6218e148bb3ed0a6e
View on Chainz β†—

Height

#2,290,096

Difficulty

10.955475

Transactions

1

Size

201 B

Version

2

Bits

0af49a01

Nonce

452,081,025

Timestamp

9/10/2017, 2:51:54 AM

Confirmations

4,543,758

Mined by

⛏️ P2SHAUMpZvDCmyd4p6rHfVeoFH3CEWrJFc3Kkt

Merkle Root

ae6fd257507ef7b4b3934a9f098cccfa1481ee06437f1b1f3673389bdc31102e
Transactions (1)
Coinbaseae6fd257507ef7…73389bdc31102e
1 in β†’ 1 out8.3200 XPM110 B
AUMpZvDC…rJFc3Kkt
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.

8.481 Γ— 10⁹⁢(97-digit number)
84818406830163304437…69533842809842175999
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
8.481 Γ— 10⁹⁢(97-digit number)
84818406830163304437…69533842809842175999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.481 Γ— 10⁹⁢(97-digit number)
84818406830163304437…69533842809842176001
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
1.696 Γ— 10⁹⁷(98-digit number)
16963681366032660887…39067685619684351999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.696 Γ— 10⁹⁷(98-digit number)
16963681366032660887…39067685619684352001
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
3.392 Γ— 10⁹⁷(98-digit number)
33927362732065321774…78135371239368703999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.392 Γ— 10⁹⁷(98-digit number)
33927362732065321774…78135371239368704001
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
6.785 Γ— 10⁹⁷(98-digit number)
67854725464130643549…56270742478737407999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.785 Γ— 10⁹⁷(98-digit number)
67854725464130643549…56270742478737408001
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
1.357 Γ— 10⁹⁸(99-digit number)
13570945092826128709…12541484957474815999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.357 Γ— 10⁹⁸(99-digit number)
13570945092826128709…12541484957474816001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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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