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Block #352,143

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/10/2014, 4:07:23 AM Β· Difficulty 10.3019 Β· 6,473,197 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7739762d24da66927eeb87e81b2b7e5552b3916a6648f31635512dbd7c99b0c9
View on Chainz β†—

Height

#352,143

Difficulty

10.301905

Transactions

2

Size

391 B

Version

2

Bits

0a4d49a3

Nonce

44,122

Timestamp

1/10/2014, 4:07:23 AM

Confirmations

6,473,197

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

6d910c087a3ba99faea6f6b0948ff5c1a52cfa00463bd684986cf1b1b56498a9
Transactions (2)
Coinbase0edf29da678621…d2914a0983d27f
1 in β†’ 1 out9.4200 XPM110 B
AeKNrjNj…1NEq95Ta
ad53d059323488…704c1c217a9c71
1 in β†’ 1 out1.0025 XPM191 B
AYeRLDn5…7XRnD3jN
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.

8.424 Γ— 10⁹³(94-digit number)
84244170309297167117…80845581054414919679
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
8.424 Γ— 10⁹³(94-digit number)
84244170309297167117…80845581054414919679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.424 Γ— 10⁹³(94-digit number)
84244170309297167117…80845581054414919681
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
1.684 Γ— 10⁹⁴(95-digit number)
16848834061859433423…61691162108829839359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.684 Γ— 10⁹⁴(95-digit number)
16848834061859433423…61691162108829839361
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
3.369 Γ— 10⁹⁴(95-digit number)
33697668123718866846…23382324217659678719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.369 Γ— 10⁹⁴(95-digit number)
33697668123718866846…23382324217659678721
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
6.739 Γ— 10⁹⁴(95-digit number)
67395336247437733693…46764648435319357439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.739 Γ— 10⁹⁴(95-digit number)
67395336247437733693…46764648435319357441
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
1.347 Γ— 10⁹⁡(96-digit number)
13479067249487546738…93529296870638714879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.347 Γ— 10⁹⁡(96-digit number)
13479067249487546738…93529296870638714881
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:57,846,825 XPMΒ·at block #6,825,339 Β· updates every 60s
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