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Block #1,840,389

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/8/2016, 3:38:36 PM Β· Difficulty 10.6389 Β· 4,993,057 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0ed9c95c193affeac3b946a5c3055a5a311842fd2fb9e70d70bd0cf927b6d018
View on Chainz β†—

Height

#1,840,389

Difficulty

10.638885

Transactions

2

Size

2.15 KB

Version

2

Bits

0aa38df2

Nonce

1,807,872,038

Timestamp

11/8/2016, 3:38:36 PM

Confirmations

4,993,057

Mined by

⛏️ P2SHAW9X5q1DPrLAVuXvSrA3mvf9a3FSJ8eqdL

Merkle Root

da8e3e7714db7717507b45cc57c1807df0f6ea956fdc3d11a69d8b71bc499b1c
Transactions (2)
Coinbasefd1eaa4cb7ec52…0df8ba3bd7ac41
1 in β†’ 1 out8.8500 XPM109 B
AW9X5q1D…FSJ8eqdL
e330ff2c26a3d4…760e589c0e1c15
13 in β†’ 2 out6000.0100 XPM1.96 KB
ASxPd6m4…knQYYUPhAcAv3ACB…xyn4r9Hk
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.

2.580 Γ— 10⁹³(94-digit number)
25808080149731085297…25557464494606356479
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
2.580 Γ— 10⁹³(94-digit number)
25808080149731085297…25557464494606356479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.580 Γ— 10⁹³(94-digit number)
25808080149731085297…25557464494606356481
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
5.161 Γ— 10⁹³(94-digit number)
51616160299462170595…51114928989212712959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.161 Γ— 10⁹³(94-digit number)
51616160299462170595…51114928989212712961
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
1.032 Γ— 10⁹⁴(95-digit number)
10323232059892434119…02229857978425425919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.032 Γ— 10⁹⁴(95-digit number)
10323232059892434119…02229857978425425921
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
2.064 Γ— 10⁹⁴(95-digit number)
20646464119784868238…04459715956850851839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.064 Γ— 10⁹⁴(95-digit number)
20646464119784868238…04459715956850851841
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
4.129 Γ— 10⁹⁴(95-digit number)
41292928239569736476…08919431913701703679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.129 Γ— 10⁹⁴(95-digit number)
41292928239569736476…08919431913701703681
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:57,911,766 XPMΒ·at block #6,833,445 Β· updates every 60s
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