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Block #102,591

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/7/2013, 4:59:14 AM Β· Difficulty 9.4989 Β· 6,713,438 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2e6577f93ff7155be76d9e56a30d049e2451ff09bbb033695f7f9940a17f0c00
View on Chainz β†—

Height

#102,591

Difficulty

9.498889

Transactions

1

Size

199 B

Version

2

Bits

097fb729

Nonce

199,980

Timestamp

8/7/2013, 4:59:14 AM

Confirmations

6,713,438

Mined by

⛏️ P2SHAeEXQxqG1a9HUoHobjrNQ1M2oHJ2q5dxWc

Merkle Root

6b6973bef8dee403e7cc1b9581ad5fc29b359413fed61b44fb856813c6dd5a53
Transactions (1)
Coinbase6b6973bef8dee4…856813c6dd5a53
1 in β†’ 1 out11.0700 XPM109 B
AeEXQxqG…J2q5dxWc
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.

4.191 Γ— 10⁹⁴(95-digit number)
41911092527339887470…87759280912147184639
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
4.191 Γ— 10⁹⁴(95-digit number)
41911092527339887470…87759280912147184639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.191 Γ— 10⁹⁴(95-digit number)
41911092527339887470…87759280912147184641
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
8.382 Γ— 10⁹⁴(95-digit number)
83822185054679774940…75518561824294369279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.382 Γ— 10⁹⁴(95-digit number)
83822185054679774940…75518561824294369281
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
1.676 Γ— 10⁹⁡(96-digit number)
16764437010935954988…51037123648588738559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.676 Γ— 10⁹⁡(96-digit number)
16764437010935954988…51037123648588738561
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
3.352 Γ— 10⁹⁡(96-digit number)
33528874021871909976…02074247297177477119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.352 Γ— 10⁹⁡(96-digit number)
33528874021871909976…02074247297177477121
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
6.705 Γ— 10⁹⁡(96-digit number)
67057748043743819952…04148494594354954239
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:57,772,345 XPMΒ·at block #6,816,028 Β· updates every 60s
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