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Block #2,684,915

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/30/2018, 8:15:01 PM Β· Difficulty 11.6915 Β· 4,153,383 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
46873cb3936a66d3eb350ba1f165aaf85dd9aee373bcf982221dd96f61d9cdde
View on Chainz β†—

Height

#2,684,915

Difficulty

11.691508

Transactions

2

Size

1.14 KB

Version

2

Bits

0bb106ac

Nonce

126,020,576

Timestamp

5/30/2018, 8:15:01 PM

Confirmations

4,153,383

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

03ad8add85e7f5a7353650a912904faf0d60c2e9d93ca9ebe0d034b37d1f2534
Transactions (2)
Coinbaseb543b27878657a…97f06365a36653
1 in β†’ 1 out7.3100 XPM110 B
Adqah8zh…1WwoHJ9t
9e557fbb49ef59…21c35b4cb7ee42
6 in β†’ 2 out1.9843 XPM965 B
AbiZw7N1…HPacQJfkAZD4meFJ…9HXXqNU7
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.

1.124 Γ— 10⁹⁢(97-digit number)
11248174783386429327…43284657528843986559
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
1.124 Γ— 10⁹⁢(97-digit number)
11248174783386429327…43284657528843986559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.124 Γ— 10⁹⁢(97-digit number)
11248174783386429327…43284657528843986561
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
2.249 Γ— 10⁹⁢(97-digit number)
22496349566772858655…86569315057687973119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.249 Γ— 10⁹⁢(97-digit number)
22496349566772858655…86569315057687973121
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
4.499 Γ— 10⁹⁢(97-digit number)
44992699133545717311…73138630115375946239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.499 Γ— 10⁹⁢(97-digit number)
44992699133545717311…73138630115375946241
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
8.998 Γ— 10⁹⁢(97-digit number)
89985398267091434623…46277260230751892479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.998 Γ— 10⁹⁢(97-digit number)
89985398267091434623…46277260230751892481
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
1.799 Γ— 10⁹⁷(98-digit number)
17997079653418286924…92554520461503784959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.799 Γ— 10⁹⁷(98-digit number)
17997079653418286924…92554520461503784961
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
3.599 Γ— 10⁹⁷(98-digit number)
35994159306836573849…85109040923007569919
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:57,950,660 XPMΒ·at block #6,838,297 Β· updates every 60s
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