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Block #2,214,751

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/20/2017, 11:05:04 AM Β· Difficulty 10.9436 Β· 4,628,245 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e16baca67008639e546dadc6920a7fe16d241ea2a964407b8f4f6066e155cbaf
View on Chainz β†—

Height

#2,214,751

Difficulty

10.943630

Transactions

2

Size

2.26 KB

Version

2

Bits

0af191c1

Nonce

702,661,419

Timestamp

7/20/2017, 11:05:04 AM

Confirmations

4,628,245

Mined by

⛏️ P2SHAKypC197ot7c1wrZSEt664w5Pb8Hf4u1pV

Merkle Root

07807f0bf5cc48da8a24847e49445205114ed2b4ec1bffd3a7a907b4492486cd
Transactions (2)
Coinbase82d249e313fd32…26fd5a81ce57ff
1 in β†’ 1 out8.3700 XPM110 B
AKypC197…8Hf4u1pV
3f1c38d14f4ab6…32189f886e0462
14 in β†’ 1 out88.0000 XPM2.07 KB
Ae9e8Eqy…RcAw15Xj
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.

2.418 Γ— 10⁹⁸(99-digit number)
24186224872955547798…96338284007298170879
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
2.418 Γ— 10⁹⁸(99-digit number)
24186224872955547798…96338284007298170879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.418 Γ— 10⁹⁸(99-digit number)
24186224872955547798…96338284007298170881
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
4.837 Γ— 10⁹⁸(99-digit number)
48372449745911095597…92676568014596341759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.837 Γ— 10⁹⁸(99-digit number)
48372449745911095597…92676568014596341761
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
9.674 Γ— 10⁹⁸(99-digit number)
96744899491822191195…85353136029192683519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.674 Γ— 10⁹⁸(99-digit number)
96744899491822191195…85353136029192683521
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
1.934 Γ— 10⁹⁹(100-digit number)
19348979898364438239…70706272058385367039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.934 Γ— 10⁹⁹(100-digit number)
19348979898364438239…70706272058385367041
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
3.869 Γ— 10⁹⁹(100-digit number)
38697959796728876478…41412544116770734079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.869 Γ— 10⁹⁹(100-digit number)
38697959796728876478…41412544116770734081
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
7.739 Γ— 10⁹⁹(100-digit number)
77395919593457752956…82825088233541468159
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:57,988,323 XPMΒ·at block #6,842,995 Β· updates every 60s
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