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Block #2,881,084

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/14/2018, 6:52:00 PM Β· Difficulty 11.6294 Β· 3,961,228 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
30cd1755632d3fbad08620ab7d45908618d1a34288de82bb73d15ecf559dc1b1
View on Chainz β†—

Height

#2,881,084

Difficulty

11.629351

Transactions

1

Size

200 B

Version

2

Bits

0ba11d2b

Nonce

1,845,885,861

Timestamp

10/14/2018, 6:52:00 PM

Confirmations

3,961,228

Mined by

⛏️ P2SHANPNCFxceqK1cdKqC91ihFPnxT4CgSQStQ

Merkle Root

034677cfebbf37245250a71b9f0d534945a4dacc464f37ee64d0173a1e3a27a3
Transactions (1)
Coinbase034677cfebbf37…d0173a1e3a27a3
1 in β†’ 1 out7.3800 XPM110 B
ANPNCFxc…4CgSQStQ
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.

3.257 Γ— 10⁹⁡(96-digit number)
32574523172048595010…35980287260975325989
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
3.257 Γ— 10⁹⁡(96-digit number)
32574523172048595010…35980287260975325989
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.257 Γ— 10⁹⁡(96-digit number)
32574523172048595010…35980287260975325991
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
6.514 Γ— 10⁹⁡(96-digit number)
65149046344097190021…71960574521950651979
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.514 Γ— 10⁹⁡(96-digit number)
65149046344097190021…71960574521950651981
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
1.302 Γ— 10⁹⁢(97-digit number)
13029809268819438004…43921149043901303959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.302 Γ— 10⁹⁢(97-digit number)
13029809268819438004…43921149043901303961
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
2.605 Γ— 10⁹⁢(97-digit number)
26059618537638876008…87842298087802607919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.605 Γ— 10⁹⁢(97-digit number)
26059618537638876008…87842298087802607921
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
5.211 Γ— 10⁹⁢(97-digit number)
52119237075277752017…75684596175605215839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.211 Γ— 10⁹⁢(97-digit number)
52119237075277752017…75684596175605215841
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
1.042 Γ— 10⁹⁷(98-digit number)
10423847415055550403…51369192351210431679
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:57,982,903 XPMΒ·at block #6,842,311 Β· updates every 60s
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