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Block #2,631,167

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/26/2018, 11:01:54 PM Β· Difficulty 11.1708 Β· 4,213,674 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
017e963f473372a88cc8575a9df1bc57aca4474981e941932cd9856a6d17084d
View on Chainz β†—

Height

#2,631,167

Difficulty

11.170835

Transactions

2

Size

574 B

Version

2

Bits

0b2bbbd4

Nonce

591,769,929

Timestamp

4/26/2018, 11:01:54 PM

Confirmations

4,213,674

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

8590e71d72ea6e37fcdc385b27ccd070f2a070079f60d480729b4c72bd74d02a
Transactions (2)
Coinbase49b735698c3192…7922eaf45c2e92
1 in β†’ 1 out8.0100 XPM110 B
Adqah8zh…1WwoHJ9t
fa223dbe2bb8ad…3e3bcf4a85a17f
2 in β†’ 2 out69.9800 XPM373 B
AJvhwU3i…seSzYSkMAFpHJhDK…hyA1PvSQ
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.

2.332 Γ— 10⁹⁷(98-digit number)
23327524890796205162…40777229866617815039
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
2.332 Γ— 10⁹⁷(98-digit number)
23327524890796205162…40777229866617815039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.332 Γ— 10⁹⁷(98-digit number)
23327524890796205162…40777229866617815041
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
4.665 Γ— 10⁹⁷(98-digit number)
46655049781592410325…81554459733235630079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.665 Γ— 10⁹⁷(98-digit number)
46655049781592410325…81554459733235630081
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
9.331 Γ— 10⁹⁷(98-digit number)
93310099563184820651…63108919466471260159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.331 Γ— 10⁹⁷(98-digit number)
93310099563184820651…63108919466471260161
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
1.866 Γ— 10⁹⁸(99-digit number)
18662019912636964130…26217838932942520319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.866 Γ— 10⁹⁸(99-digit number)
18662019912636964130…26217838932942520321
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
3.732 Γ— 10⁹⁸(99-digit number)
37324039825273928260…52435677865885040639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.732 Γ— 10⁹⁸(99-digit number)
37324039825273928260…52435677865885040641
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
7.464 Γ— 10⁹⁸(99-digit number)
74648079650547856521…04871355731770081279
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:58,003,137 XPMΒ·at block #6,844,840 Β· updates every 60s
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