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Block #2,730,984

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/2/2018, 11:23:40 AM Β· Difficulty 11.6314 Β· 4,108,890 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
918286172440b150adeb1488b92a3c1d979e1cef74da24a967896dabd26773e5
View on Chainz β†—

Height

#2,730,984

Difficulty

11.631440

Transactions

1

Size

200 B

Version

2

Bits

0ba1a613

Nonce

495,099,001

Timestamp

7/2/2018, 11:23:40 AM

Confirmations

4,108,890

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

91b4a83d9c03023f1a97ecf458c82127dd8dc49661196da04d272052273d8c4d
Transactions (1)
Coinbase91b4a83d9c0302…272052273d8c4d
1 in β†’ 1 out7.3800 XPM110 B
AZtxQr2F…7grUWrUz
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.

2.842 Γ— 10⁹⁴(95-digit number)
28422298039108905314…78410470219021171199
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
2.842 Γ— 10⁹⁴(95-digit number)
28422298039108905314…78410470219021171199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.842 Γ— 10⁹⁴(95-digit number)
28422298039108905314…78410470219021171201
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
5.684 Γ— 10⁹⁴(95-digit number)
56844596078217810629…56820940438042342399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.684 Γ— 10⁹⁴(95-digit number)
56844596078217810629…56820940438042342401
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
1.136 Γ— 10⁹⁡(96-digit number)
11368919215643562125…13641880876084684799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.136 Γ— 10⁹⁡(96-digit number)
11368919215643562125…13641880876084684801
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
2.273 Γ— 10⁹⁡(96-digit number)
22737838431287124251…27283761752169369599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.273 Γ— 10⁹⁡(96-digit number)
22737838431287124251…27283761752169369601
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
4.547 Γ— 10⁹⁡(96-digit number)
45475676862574248503…54567523504338739199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.547 Γ— 10⁹⁡(96-digit number)
45475676862574248503…54567523504338739201
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
9.095 Γ— 10⁹⁡(96-digit number)
90951353725148497007…09135047008677478399
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:57,963,293 XPMΒ·at block #6,839,873 Β· updates every 60s
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