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Block #2,795,628

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/15/2018, 9:25:54 PM Β· Difficulty 11.6801 Β· 4,047,586 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1bd5c99f2ba5dc0efd2c88511ff971c3d87c2bae19a1bd7e087041c1d8777724
View on Chainz β†—

Height

#2,795,628

Difficulty

11.680064

Transactions

1

Size

200 B

Version

2

Bits

0bae18af

Nonce

867,906,592

Timestamp

8/15/2018, 9:25:54 PM

Confirmations

4,047,586

Mined by

⛏️ P2SHASJiq1mgQzA6Sqe7eRfHV9SVXauMtUXpvJ

Merkle Root

3ae06f593b6d7159e1b72b1c254ae7f64a16567dc5f40d13853bc2b157a75792
Transactions (1)
Coinbase3ae06f593b6d71…3bc2b157a75792
1 in β†’ 1 out7.3200 XPM110 B
ASJiq1mg…uMtUXpvJ
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.

8.630 Γ— 10⁹⁡(96-digit number)
86309727892854468015…54691833188436587519
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
8.630 Γ— 10⁹⁡(96-digit number)
86309727892854468015…54691833188436587519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.630 Γ— 10⁹⁡(96-digit number)
86309727892854468015…54691833188436587521
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
1.726 Γ— 10⁹⁢(97-digit number)
17261945578570893603…09383666376873175039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.726 Γ— 10⁹⁢(97-digit number)
17261945578570893603…09383666376873175041
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
3.452 Γ— 10⁹⁢(97-digit number)
34523891157141787206…18767332753746350079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.452 Γ— 10⁹⁢(97-digit number)
34523891157141787206…18767332753746350081
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
6.904 Γ— 10⁹⁢(97-digit number)
69047782314283574412…37534665507492700159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.904 Γ— 10⁹⁢(97-digit number)
69047782314283574412…37534665507492700161
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
1.380 Γ— 10⁹⁷(98-digit number)
13809556462856714882…75069331014985400319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.380 Γ— 10⁹⁷(98-digit number)
13809556462856714882…75069331014985400321
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
2.761 Γ— 10⁹⁷(98-digit number)
27619112925713429764…50138662029970800639
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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