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Block #1,125,833

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/25/2015, 5:18:24 AM Β· Difficulty 10.9303 Β· 5,669,724 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
812d5597b3fed9ea53711aef9cf6e12e249a8990808da25eef8e3fa1d4e329b3
View on Chainz β†—

Height

#1,125,833

Difficulty

10.930255

Transactions

2

Size

1019 B

Version

2

Bits

0aee252e

Nonce

592,944,367

Timestamp

6/25/2015, 5:18:24 AM

Confirmations

5,669,724

Mined by

⛏️ P2SHAJ1HPLFH43w448eir8ShdR8oFDAvSxsvyP

Merkle Root

3365151f38f87fefdb57ce63188b62e7cec7946d21f9fbdfaccf44ca1021fa25
Transactions (2)
Coinbaseb161f3566cb9d7…fb574a8566de67
1 in β†’ 1 out8.3700 XPM110 B
AJ1HPLFH…AvSxsvyP
8ca7e22b29f528…6dbf8f68c8ec07
5 in β†’ 2 out1099.7739 XPM819 B
ARpjHv1k…4F9NvuWNAJPfd4Mk…Z7SutKNM
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.

1.120 Γ— 10⁹⁡(96-digit number)
11200707796518350942…85177294158047039999
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
1.120 Γ— 10⁹⁡(96-digit number)
11200707796518350942…85177294158047039999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.120 Γ— 10⁹⁡(96-digit number)
11200707796518350942…85177294158047040001
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
2.240 Γ— 10⁹⁡(96-digit number)
22401415593036701884…70354588316094079999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.240 Γ— 10⁹⁡(96-digit number)
22401415593036701884…70354588316094080001
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
4.480 Γ— 10⁹⁡(96-digit number)
44802831186073403769…40709176632188159999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.480 Γ— 10⁹⁡(96-digit number)
44802831186073403769…40709176632188160001
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
8.960 Γ— 10⁹⁡(96-digit number)
89605662372146807538…81418353264376319999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.960 Γ— 10⁹⁡(96-digit number)
89605662372146807538…81418353264376320001
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
1.792 Γ— 10⁹⁢(97-digit number)
17921132474429361507…62836706528752639999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.792 Γ— 10⁹⁢(97-digit number)
17921132474429361507…62836706528752640001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
3.584 Γ— 10⁹⁢(97-digit number)
35842264948858723015…25673413057505279999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,608,521 XPMΒ·at block #6,795,556 Β· updates every 60s
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