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Block #2,088,480

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/26/2017, 9:06:19 AM Β· Difficulty 10.8754 Β· 4,726,666 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0999ff307b0a90fe6645bf7bf44b2a7ea8cbb47159aaae8da6de74d58d8f8733
View on Chainz β†—

Height

#2,088,480

Difficulty

10.875401

Transactions

1

Size

198 B

Version

2

Bits

0ae01a4d

Nonce

301,704,050

Timestamp

4/26/2017, 9:06:19 AM

Confirmations

4,726,666

Mined by

⛏️ P2SHAG94RFpeBU8M9BzRgcSaDhsFY7QXtnbsQr

Merkle Root

a254a8a268124cb168e0a24cc34a3c5c44f7a171d0afff4585f4f1cd9732ed0a
Transactions (1)
Coinbasea254a8a268124c…f4f1cd9732ed0a
1 in β†’ 1 out8.4400 XPM109 B
AG94RFpe…QXtnbsQr
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.

8.493 Γ— 10⁹²(93-digit number)
84931193866024380449…65726403542013388319
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
8.493 Γ— 10⁹²(93-digit number)
84931193866024380449…65726403542013388319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.493 Γ— 10⁹²(93-digit number)
84931193866024380449…65726403542013388321
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
1.698 Γ— 10⁹³(94-digit number)
16986238773204876089…31452807084026776639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.698 Γ— 10⁹³(94-digit number)
16986238773204876089…31452807084026776641
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
3.397 Γ— 10⁹³(94-digit number)
33972477546409752179…62905614168053553279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.397 Γ— 10⁹³(94-digit number)
33972477546409752179…62905614168053553281
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
6.794 Γ— 10⁹³(94-digit number)
67944955092819504359…25811228336107106559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.794 Γ— 10⁹³(94-digit number)
67944955092819504359…25811228336107106561
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
1.358 Γ— 10⁹⁴(95-digit number)
13588991018563900871…51622456672214213119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.358 Γ— 10⁹⁴(95-digit number)
13588991018563900871…51622456672214213121
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:57,765,262 XPMΒ·at block #6,815,145 Β· updates every 60s
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