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Block #240,416

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/2/2013, 2:46:52 PM Β· Difficulty 9.9566 Β· 6,570,236 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c1469c3808aa4ce894001d94faefa35b7d3e220ee0b4d20cfca91c89630f4104
View on Chainz β†—

Height

#240,416

Difficulty

9.956581

Transactions

1

Size

196 B

Version

2

Bits

09f4e27a

Nonce

3,825

Timestamp

11/2/2013, 2:46:52 PM

Confirmations

6,570,236

Mined by

⛏️ P2SHAZnPYg8XCxcZrU372xpdUULdGsaL9G3mAi

Merkle Root

003960c2d32f895da4122fbdf112472b9df1df8e6d76e6e094a880da0840809d
Transactions (1)
Coinbase003960c2d32f89…a880da0840809d
1 in β†’ 1 out10.0700 XPM109 B
AZnPYg8X…aL9G3mAi
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.

1.889 Γ— 10⁸⁷(88-digit number)
18893378419384304144…76678034457771425859
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
1.889 Γ— 10⁸⁷(88-digit number)
18893378419384304144…76678034457771425859
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.889 Γ— 10⁸⁷(88-digit number)
18893378419384304144…76678034457771425861
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
3.778 Γ— 10⁸⁷(88-digit number)
37786756838768608289…53356068915542851719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.778 Γ— 10⁸⁷(88-digit number)
37786756838768608289…53356068915542851721
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
7.557 Γ— 10⁸⁷(88-digit number)
75573513677537216578…06712137831085703439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.557 Γ— 10⁸⁷(88-digit number)
75573513677537216578…06712137831085703441
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
1.511 Γ— 10⁸⁸(89-digit number)
15114702735507443315…13424275662171406879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.511 Γ— 10⁸⁸(89-digit number)
15114702735507443315…13424275662171406881
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
3.022 Γ— 10⁸⁸(89-digit number)
30229405471014886631…26848551324342813759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.022 Γ— 10⁸⁸(89-digit number)
30229405471014886631…26848551324342813761
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:57,729,306 XPMΒ·at block #6,810,651 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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