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Block #105,867

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/8/2013, 6:04:04 PM Β· Difficulty 9.5935 Β· 6,700,896 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3751d7e2904b96346366d6dc5073f180c44aaa927a5a7bd6fba85a9cba95f04b
View on Chainz β†—

Height

#105,867

Difficulty

9.593541

Transactions

2

Size

472 B

Version

2

Bits

0997f246

Nonce

260,799

Timestamp

8/8/2013, 6:04:04 PM

Confirmations

6,700,896

Mined by

⛏️ P2SHAZ29sR79QusQVNF36wMX1odggdnKVqwKGr

Merkle Root

c3c140c1253347019136a3c6e9fad57fc9201d8f8aabe99d646be81e667d0fd3
Transactions (2)
Coinbase6b04f8c0d6def7…7594d8a187f084
1 in β†’ 1 out10.8600 XPM109 B
AZ29sR79…nKVqwKGr
d4db866db73642…d9e1d50a7fbcd0
2 in β†’ 1 out22.1100 XPM272 B
AKfeR8gS…LNjUzaey
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.

5.124 Γ— 10⁹⁷(98-digit number)
51241863357861679666…59502624023390404919
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
5.124 Γ— 10⁹⁷(98-digit number)
51241863357861679666…59502624023390404919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.124 Γ— 10⁹⁷(98-digit number)
51241863357861679666…59502624023390404921
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
1.024 Γ— 10⁹⁸(99-digit number)
10248372671572335933…19005248046780809839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.024 Γ— 10⁹⁸(99-digit number)
10248372671572335933…19005248046780809841
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
2.049 Γ— 10⁹⁸(99-digit number)
20496745343144671866…38010496093561619679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.049 Γ— 10⁹⁸(99-digit number)
20496745343144671866…38010496093561619681
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
4.099 Γ— 10⁹⁸(99-digit number)
40993490686289343733…76020992187123239359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.099 Γ— 10⁹⁸(99-digit number)
40993490686289343733…76020992187123239361
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
8.198 Γ— 10⁹⁸(99-digit number)
81986981372578687466…52041984374246478719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.198 Γ— 10⁹⁸(99-digit number)
81986981372578687466…52041984374246478721
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:57,698,205 XPMΒ·at block #6,806,762 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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