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Block #2,111,593

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/11/2017, 1:55:32 PM Β· Difficulty 10.9028 Β· 4,730,351 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
476adc341937de241aa540c6da8072d6b98f704e28039ba6906d2a214c42ca02
View on Chainz β†—

Height

#2,111,593

Difficulty

10.902838

Transactions

2

Size

425 B

Version

2

Bits

0ae7205f

Nonce

1,625,145,310

Timestamp

5/11/2017, 1:55:32 PM

Confirmations

4,730,351

Mined by

⛏️ P2SHAbwcxMdRvxJasKcXSq1SWBj8LmpjsN788s

Merkle Root

d6638194a481b497038822ead3a50724833a18b5332bea03e07abbba4f98ffcc
Transactions (2)
Coinbase724424022c7207…f8e7f8d4990cfa
1 in β†’ 1 out8.4100 XPM109 B
AbwcxMdR…pjsN788s
42d43534bcf619…496934ca832e8f
1 in β†’ 2 out150762.6088 XPM226 B
AZ7Cgvp2…3iVatWnqANdsz5uE…NDhTWwEi
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.

4.838 Γ— 10⁹⁴(95-digit number)
48385998566231116399…79637850287827245399
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
4.838 Γ— 10⁹⁴(95-digit number)
48385998566231116399…79637850287827245399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.838 Γ— 10⁹⁴(95-digit number)
48385998566231116399…79637850287827245401
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
9.677 Γ— 10⁹⁴(95-digit number)
96771997132462232799…59275700575654490799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.677 Γ— 10⁹⁴(95-digit number)
96771997132462232799…59275700575654490801
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
1.935 Γ— 10⁹⁡(96-digit number)
19354399426492446559…18551401151308981599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.935 Γ— 10⁹⁡(96-digit number)
19354399426492446559…18551401151308981601
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
3.870 Γ— 10⁹⁡(96-digit number)
38708798852984893119…37102802302617963199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.870 Γ— 10⁹⁡(96-digit number)
38708798852984893119…37102802302617963201
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
7.741 Γ— 10⁹⁡(96-digit number)
77417597705969786239…74205604605235926399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.741 Γ— 10⁹⁡(96-digit number)
77417597705969786239…74205604605235926401
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:57,979,933 XPMΒ·at block #6,841,943 Β· updates every 60s
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