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Block #2,706,595

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/15/2018, 5:55:28 PM Β· Difficulty 11.6078 Β· 4,126,333 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
baa784a5fe9c04de8226bdf1f56da9887619d9657f6c5cd749eb67cedf8e1cc4
View on Chainz β†—

Height

#2,706,595

Difficulty

11.607765

Transactions

2

Size

1.14 KB

Version

2

Bits

0b9b967d

Nonce

70,252,062

Timestamp

6/15/2018, 5:55:28 PM

Confirmations

4,126,333

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

294be52994acb5a550b51b1de3f16574e7bf8ef051fd5c51cacc65db3e34220d
Transactions (2)
Coinbase32f3811bf5a92e…212d0a69d6007f
1 in β†’ 1 out7.4300 XPM110 B
AZtxQr2F…7grUWrUz
81977decfa5fd2…b941017bc0e064
6 in β†’ 2 out120.6612 XPM968 B
AUsyS9Y4…WM4tVcezAd5kuZzj…FTtsv8uP
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.

9.350 Γ— 10⁹⁴(95-digit number)
93503381259073226079…86775409607785798879
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
9.350 Γ— 10⁹⁴(95-digit number)
93503381259073226079…86775409607785798879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.350 Γ— 10⁹⁴(95-digit number)
93503381259073226079…86775409607785798881
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
1.870 Γ— 10⁹⁡(96-digit number)
18700676251814645215…73550819215571597759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.870 Γ— 10⁹⁡(96-digit number)
18700676251814645215…73550819215571597761
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
3.740 Γ— 10⁹⁡(96-digit number)
37401352503629290431…47101638431143195519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.740 Γ— 10⁹⁡(96-digit number)
37401352503629290431…47101638431143195521
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
7.480 Γ— 10⁹⁡(96-digit number)
74802705007258580863…94203276862286391039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.480 Γ— 10⁹⁡(96-digit number)
74802705007258580863…94203276862286391041
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
1.496 Γ— 10⁹⁢(97-digit number)
14960541001451716172…88406553724572782079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.496 Γ— 10⁹⁢(97-digit number)
14960541001451716172…88406553724572782081
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
2.992 Γ— 10⁹⁢(97-digit number)
29921082002903432345…76813107449145564159
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:57,907,600 XPMΒ·at block #6,832,927 Β· updates every 60s
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