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Block #2,640,884

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/1/2018, 4:02:57 AM Β· Difficulty 11.5988 Β· 4,164,285 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
53aaeea8589ef21e9b1d1a80c352149e38ccc1a4e0ae1f160119212fcbf398b2
View on Chainz β†—

Height

#2,640,884

Difficulty

11.598804

Transactions

2

Size

3.03 KB

Version

2

Bits

0b994b3d

Nonce

1,945,695,858

Timestamp

5/1/2018, 4:02:57 AM

Confirmations

4,164,285

Mined by

⛏️ P2SHAX89qXquqnLdNx69SA8yRTy8u1EaLB9ER8

Merkle Root

847b7bf964b86234c37544ad2449348847284e13a0266ea6c7b52224c1d56e46
Transactions (2)
Coinbasec0694d23f7389e…3adf3bd6cc5c80
1 in β†’ 1 out7.4600 XPM110 B
AX89qXqu…EaLB9ER8
333bb7b3a3294b…17d2801eb21676
19 in β†’ 2 out199.9100 XPM2.83 KB
ASx7PWVz…1Q54uCeLAGbUPi3v…cpf6KNJa
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.

7.721 Γ— 10⁹⁴(95-digit number)
77218018635341413861…43096883914619703359
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
7.721 Γ— 10⁹⁴(95-digit number)
77218018635341413861…43096883914619703359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.721 Γ— 10⁹⁴(95-digit number)
77218018635341413861…43096883914619703361
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
1.544 Γ— 10⁹⁡(96-digit number)
15443603727068282772…86193767829239406719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.544 Γ— 10⁹⁡(96-digit number)
15443603727068282772…86193767829239406721
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
3.088 Γ— 10⁹⁡(96-digit number)
30887207454136565544…72387535658478813439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.088 Γ— 10⁹⁡(96-digit number)
30887207454136565544…72387535658478813441
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
6.177 Γ— 10⁹⁡(96-digit number)
61774414908273131089…44775071316957626879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.177 Γ— 10⁹⁡(96-digit number)
61774414908273131089…44775071316957626881
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
1.235 Γ— 10⁹⁢(97-digit number)
12354882981654626217…89550142633915253759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.235 Γ— 10⁹⁢(97-digit number)
12354882981654626217…89550142633915253761
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
2.470 Γ— 10⁹⁢(97-digit number)
24709765963309252435…79100285267830507519
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:57,685,420 XPMΒ·at block #6,805,168 Β· updates every 60s
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