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Block #276,028

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/26/2013, 11:49:10 PM Β· Difficulty 9.9622 Β· 6,533,335 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
81daaa41a6653c0c041c5b03da5c1b71d77819e65d31474702645247f9fcde0f
View on Chainz β†—

Height

#276,028

Difficulty

9.962229

Transactions

2

Size

1.14 KB

Version

2

Bits

09f654ac

Nonce

43,186

Timestamp

11/26/2013, 11:49:10 PM

Confirmations

6,533,335

Mined by

⛏️ P2SHAWVqgA8uvNUvjtFUDG9gCbhxgyVTZ1ARYK

Merkle Root

4fa9d9c38462db63c9d61be4bb18587ca6bbf7ed5bf2d0f3f94834ffa037d7e2
Transactions (2)
Coinbase850ea4d25f743f…3ab62fd6639da7
1 in β†’ 1 out10.0700 XPM109 B
AWVqgA8u…VTZ1ARYK
7e3221ad0e90ff…10df2e142c1e40
6 in β†’ 2 out2.0372 XPM965 B
AX3gi1Mo…4v25skFXAMhgGBr4…RWu7zMiM
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.

8.015 Γ— 10⁹⁢(97-digit number)
80150760206619226821…96855617781523141119
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
8.015 Γ— 10⁹⁢(97-digit number)
80150760206619226821…96855617781523141119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.015 Γ— 10⁹⁢(97-digit number)
80150760206619226821…96855617781523141121
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
1.603 Γ— 10⁹⁷(98-digit number)
16030152041323845364…93711235563046282239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.603 Γ— 10⁹⁷(98-digit number)
16030152041323845364…93711235563046282241
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
3.206 Γ— 10⁹⁷(98-digit number)
32060304082647690728…87422471126092564479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.206 Γ— 10⁹⁷(98-digit number)
32060304082647690728…87422471126092564481
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
6.412 Γ— 10⁹⁷(98-digit number)
64120608165295381457…74844942252185128959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.412 Γ— 10⁹⁷(98-digit number)
64120608165295381457…74844942252185128961
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
1.282 Γ— 10⁹⁸(99-digit number)
12824121633059076291…49689884504370257919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.282 Γ— 10⁹⁸(99-digit number)
12824121633059076291…49689884504370257921
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:57,718,972 XPMΒ·at block #6,809,362 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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