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Block #205,471

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/12/2013, 4:20:44 AM Β· Difficulty 9.8999 Β· 6,589,485 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e5d69b254c205a52e82c24c259b715f9731c899764eb0717cae4961da5320b4a
View on Chainz β†—

Height

#205,471

Difficulty

9.899918

Transactions

2

Size

358 B

Version

2

Bits

09e66100

Nonce

90,119

Timestamp

10/12/2013, 4:20:44 AM

Confirmations

6,589,485

Mined by

⛏️ P2SHAFvfCa1WUvxPh1KkHgJxPR6DVF3pZgbFWa

Merkle Root

adc9656914341e4d6c443e84789b6a17e02584183259f3b301ece16ce4046a97
Transactions (2)
Coinbasee186ed6b100f5d…41458ca19ca295
1 in β†’ 1 out10.2000 XPM110 B
AFvfCa1W…3pZgbFWa
16d39485c038f9…de4fdbcf3d441a
1 in β†’ 1 out10.2300 XPM158 B
ASRGgVvy…qJdDY3Pw
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.

4.234 Γ— 10⁹⁡(96-digit number)
42345054319343150923…03878537382869819399
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
4.234 Γ— 10⁹⁡(96-digit number)
42345054319343150923…03878537382869819399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.234 Γ— 10⁹⁡(96-digit number)
42345054319343150923…03878537382869819401
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
8.469 Γ— 10⁹⁡(96-digit number)
84690108638686301847…07757074765739638799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.469 Γ— 10⁹⁡(96-digit number)
84690108638686301847…07757074765739638801
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
1.693 Γ— 10⁹⁢(97-digit number)
16938021727737260369…15514149531479277599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.693 Γ— 10⁹⁢(97-digit number)
16938021727737260369…15514149531479277601
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
3.387 Γ— 10⁹⁢(97-digit number)
33876043455474520738…31028299062958555199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.387 Γ— 10⁹⁢(97-digit number)
33876043455474520738…31028299062958555201
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
6.775 Γ— 10⁹⁢(97-digit number)
67752086910949041477…62056598125917110399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,603,685 XPMΒ·at block #6,794,955 Β· updates every 60s
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