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Block #2,036,183

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/24/2017, 7:45:05 AM Β· Difficulty 10.6787 Β· 4,774,943 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6c5c2ed1221ebbd52150534c619204e0992aa1cb27a3d1e9be11f4cc245ec779
View on Chainz β†—

Height

#2,036,183

Difficulty

10.678732

Transactions

2

Size

424 B

Version

2

Bits

0aadc15c

Nonce

450,599,698

Timestamp

3/24/2017, 7:45:05 AM

Confirmations

4,774,943

Mined by

⛏️ P2SHARXTSavmFqVvnJGfJLbkLHL9aHrhani5mm

Merkle Root

6d33e742f053585f0c24fe69b5e8fd51b945247729ef65a53df0952291892afc
Transactions (2)
Coinbaseea535e075d3421…b53e1eeb8f45e5
1 in β†’ 1 out8.7700 XPM109 B
ARXTSavm…rhani5mm
6b91b99f649715…842bb334e85691
1 in β†’ 2 out89099.9900 XPM225 B
ATr1Dumu…8WWSPGFmAVPU2i57…kYsH8BA4
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.

8.264 Γ— 10⁹⁴(95-digit number)
82645906781060333710…13327076288662112319
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
8.264 Γ— 10⁹⁴(95-digit number)
82645906781060333710…13327076288662112319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.264 Γ— 10⁹⁴(95-digit number)
82645906781060333710…13327076288662112321
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
1.652 Γ— 10⁹⁡(96-digit number)
16529181356212066742…26654152577324224639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.652 Γ— 10⁹⁡(96-digit number)
16529181356212066742…26654152577324224641
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
3.305 Γ— 10⁹⁡(96-digit number)
33058362712424133484…53308305154648449279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.305 Γ— 10⁹⁡(96-digit number)
33058362712424133484…53308305154648449281
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
6.611 Γ— 10⁹⁡(96-digit number)
66116725424848266968…06616610309296898559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.611 Γ— 10⁹⁡(96-digit number)
66116725424848266968…06616610309296898561
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
1.322 Γ— 10⁹⁢(97-digit number)
13223345084969653393…13233220618593797119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.322 Γ— 10⁹⁢(97-digit number)
13223345084969653393…13233220618593797121
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:57,733,115 XPMΒ·at block #6,811,125 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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