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Block #2,773,299

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/31/2018, 1:31:41 PM Β· Difficulty 11.6627 Β· 4,067,486 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b93df19530a99c3932f750f01120c262893bdab252462d412de894f817b4f067
View on Chainz β†—

Height

#2,773,299

Difficulty

11.662673

Transactions

2

Size

576 B

Version

2

Bits

0ba9a4f3

Nonce

1,130,988,443

Timestamp

7/31/2018, 1:31:41 PM

Confirmations

4,067,486

Mined by

⛏️ P2SHANgTgu4XWEAmqzdcNJ8Pa4V7eLmQ8w6y69

Merkle Root

2eed8ff1eff6683df56286638855cca915ff9e3c2c524adc514935b6b6579ad7
Transactions (2)
Coinbase0faf8bb363e9aa…0ec10a8ad07922
1 in β†’ 1 out7.3500 XPM110 B
ANgTgu4X…mQ8w6y69
759736b1e58188…d5229b621b6c71
2 in β†’ 2 out64.0265 XPM375 B
AQmjqzoU…5U6sbve9AJvVZQcd…M11Meb64
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.

8.687 Γ— 10⁹⁢(97-digit number)
86870536767399351335…51754055132571279359
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
8.687 Γ— 10⁹⁢(97-digit number)
86870536767399351335…51754055132571279359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.687 Γ— 10⁹⁢(97-digit number)
86870536767399351335…51754055132571279361
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
1.737 Γ— 10⁹⁷(98-digit number)
17374107353479870267…03508110265142558719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.737 Γ— 10⁹⁷(98-digit number)
17374107353479870267…03508110265142558721
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
3.474 Γ— 10⁹⁷(98-digit number)
34748214706959740534…07016220530285117439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.474 Γ— 10⁹⁷(98-digit number)
34748214706959740534…07016220530285117441
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
6.949 Γ— 10⁹⁷(98-digit number)
69496429413919481068…14032441060570234879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.949 Γ— 10⁹⁷(98-digit number)
69496429413919481068…14032441060570234881
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
1.389 Γ— 10⁹⁸(99-digit number)
13899285882783896213…28064882121140469759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.389 Γ— 10⁹⁸(99-digit number)
13899285882783896213…28064882121140469761
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
2.779 Γ— 10⁹⁸(99-digit number)
27798571765567792427…56129764242280939519
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:57,970,626 XPMΒ·at block #6,840,784 Β· updates every 60s
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