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Block #333,049

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/28/2013, 12:21:46 PM Β· Difficulty 10.1646 Β· 6,468,277 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a479afcd176d3fd336ddc8eca78216cadb48ac30f4acfc303a212c339220e131
View on Chainz β†—

Height

#333,049

Difficulty

10.164593

Transactions

2

Size

359 B

Version

2

Bits

0a2a22c5

Nonce

228,027

Timestamp

12/28/2013, 12:21:46 PM

Confirmations

6,468,277

Mined by

⛏️ P2SHAJ1zJtHjC8xQPjnND4PtDaRGNXjKGU1wiP

Merkle Root

36ee1e71587f0a70c7b319a4cf8fa13616275200853f7c2329da72fce584f071
Transactions (2)
Coinbase5753190eec914f…18cd856ee87d38
1 in β†’ 1 out9.6700 XPM109 B
AJ1zJtHj…jKGU1wiP
6c914b3ef2c0f3…303e7973525f7a
1 in β†’ 1 out9.6700 XPM159 B
AXhxNajJ…CLP12ZGm
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.

5.000 Γ— 10⁹⁢(97-digit number)
50004002795920728974…50588922744594915999
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
5.000 Γ— 10⁹⁢(97-digit number)
50004002795920728974…50588922744594915999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.000 Γ— 10⁹⁢(97-digit number)
50004002795920728974…50588922744594916001
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
1.000 Γ— 10⁹⁷(98-digit number)
10000800559184145794…01177845489189831999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.000 Γ— 10⁹⁷(98-digit number)
10000800559184145794…01177845489189832001
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
2.000 Γ— 10⁹⁷(98-digit number)
20001601118368291589…02355690978379663999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.000 Γ— 10⁹⁷(98-digit number)
20001601118368291589…02355690978379664001
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
4.000 Γ— 10⁹⁷(98-digit number)
40003202236736583179…04711381956759327999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.000 Γ— 10⁹⁷(98-digit number)
40003202236736583179…04711381956759328001
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
8.000 Γ— 10⁹⁷(98-digit number)
80006404473473166358…09422763913518655999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.000 Γ— 10⁹⁷(98-digit number)
80006404473473166358…09422763913518656001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,654,676 XPMΒ·at block #6,801,325 Β· updates every 60s
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