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Block #2,815,433

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/29/2018, 2:49:35 PM Β· Difficulty 11.6833 Β· 4,025,002 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
de78873298821c9eda65df9fe27c3d3b1c35577ff0a73301becf9df56583b7dc
View on Chainz β†—

Height

#2,815,433

Difficulty

11.683345

Transactions

1

Size

202 B

Version

2

Bits

0baeefba

Nonce

881,839,138

Timestamp

8/29/2018, 2:49:35 PM

Confirmations

4,025,002

Mined by

⛏️ P2SHAHLPfD14HzfgBJeV7aGt2KY5f8QqL4XMxD

Merkle Root

c32a14aaec3275bbb96fe170d679a9af897105fb8a5a31e312fd8d093d2aa973
Transactions (1)
Coinbasec32a14aaec3275…fd8d093d2aa973
1 in β†’ 1 out7.3100 XPM110 B
AHLPfD14…QqL4XMxD
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.

1.039 Γ— 10⁹⁹(100-digit number)
10398339407735766346…42109441962020700159
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
1.039 Γ— 10⁹⁹(100-digit number)
10398339407735766346…42109441962020700159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.039 Γ— 10⁹⁹(100-digit number)
10398339407735766346…42109441962020700161
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
2.079 Γ— 10⁹⁹(100-digit number)
20796678815471532692…84218883924041400319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.079 Γ— 10⁹⁹(100-digit number)
20796678815471532692…84218883924041400321
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
4.159 Γ— 10⁹⁹(100-digit number)
41593357630943065385…68437767848082800639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.159 Γ— 10⁹⁹(100-digit number)
41593357630943065385…68437767848082800641
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
8.318 Γ— 10⁹⁹(100-digit number)
83186715261886130771…36875535696165601279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.318 Γ— 10⁹⁹(100-digit number)
83186715261886130771…36875535696165601281
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
1.663 Γ— 10¹⁰⁰(101-digit number)
16637343052377226154…73751071392331202559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.663 Γ— 10¹⁰⁰(101-digit number)
16637343052377226154…73751071392331202561
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
3.327 Γ— 10¹⁰⁰(101-digit number)
33274686104754452308…47502142784662405119
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:57,967,807 XPMΒ·at block #6,840,434 Β· updates every 60s
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