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Block #142,578

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/31/2013, 1:23:32 AM Β· Difficulty 9.8377 Β· 6,673,268 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ef07220d80de9cf7bff63a428ada456cabe9298dbb1dc26018f9241971c52b32
View on Chainz β†—

Height

#142,578

Difficulty

9.837660

Transactions

2

Size

2.24 KB

Version

2

Bits

09d670eb

Nonce

2,001

Timestamp

8/31/2013, 1:23:32 AM

Confirmations

6,673,268

Mined by

⛏️ P2SHAcUS2DxGQG5NYbNw1MKWNz9BF5tjEkemWq

Merkle Root

be1b2ef07b8cc3d8edc5bd8c6e66536f5e3407e16309da881a3ed91881384237
Transactions (2)
Coinbase1c42594c119967…7d2bb98e04100d
1 in β†’ 1 out10.3500 XPM109 B
AcUS2DxG…tjEkemWq
9b90de12b41a65…f81bfda1a1e20f
18 in β†’ 1 out186.3300 XPM2.05 KB
AX7HepGv…Qm28ooHF
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.

4.374 Γ— 10⁹⁴(95-digit number)
43749897479157741244…43324268393175593919
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
4.374 Γ— 10⁹⁴(95-digit number)
43749897479157741244…43324268393175593919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.374 Γ— 10⁹⁴(95-digit number)
43749897479157741244…43324268393175593921
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
8.749 Γ— 10⁹⁴(95-digit number)
87499794958315482489…86648536786351187839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.749 Γ— 10⁹⁴(95-digit number)
87499794958315482489…86648536786351187841
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
1.749 Γ— 10⁹⁡(96-digit number)
17499958991663096497…73297073572702375679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.749 Γ— 10⁹⁡(96-digit number)
17499958991663096497…73297073572702375681
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
3.499 Γ— 10⁹⁡(96-digit number)
34999917983326192995…46594147145404751359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.499 Γ— 10⁹⁡(96-digit number)
34999917983326192995…46594147145404751361
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
6.999 Γ— 10⁹⁡(96-digit number)
69999835966652385991…93188294290809502719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.999 Γ— 10⁹⁡(96-digit number)
69999835966652385991…93188294290809502721
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:57,770,878 XPMΒ·at block #6,815,845 Β· updates every 60s
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