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Block #2,687,460

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/1/2018, 5:42:04 PM Β· Difficulty 11.6801 Β· 4,155,882 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c9b546a94eb2006288dca42984d1bdb552b27bf0083f7c3245bacf6aca7ed47e
View on Chainz β†—

Height

#2,687,460

Difficulty

11.680142

Transactions

1

Size

201 B

Version

2

Bits

0bae1dc1

Nonce

598,399,795

Timestamp

6/1/2018, 5:42:04 PM

Confirmations

4,155,882

Mined by

⛏️ P2SHALXEGLKVXFZruBg1jabxUyB2erLa8A16Un

Merkle Root

4f9d5ab09d3f6341b2b3c8cc29b17f6a2d8b4d448ca15dfdc0fadc8bd2a1fde5
Transactions (1)
Coinbase4f9d5ab09d3f63…fadc8bd2a1fde5
1 in β†’ 1 out7.3200 XPM110 B
ALXEGLKV…La8A16Un
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.

9.340 Γ— 10⁹⁡(96-digit number)
93400978902315017086…79715018836306165759
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
9.340 Γ— 10⁹⁡(96-digit number)
93400978902315017086…79715018836306165759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.340 Γ— 10⁹⁡(96-digit number)
93400978902315017086…79715018836306165761
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
1.868 Γ— 10⁹⁢(97-digit number)
18680195780463003417…59430037672612331519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.868 Γ— 10⁹⁢(97-digit number)
18680195780463003417…59430037672612331521
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
3.736 Γ— 10⁹⁢(97-digit number)
37360391560926006834…18860075345224663039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.736 Γ— 10⁹⁢(97-digit number)
37360391560926006834…18860075345224663041
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
7.472 Γ— 10⁹⁢(97-digit number)
74720783121852013669…37720150690449326079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.472 Γ— 10⁹⁢(97-digit number)
74720783121852013669…37720150690449326081
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
1.494 Γ— 10⁹⁷(98-digit number)
14944156624370402733…75440301380898652159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.494 Γ— 10⁹⁷(98-digit number)
14944156624370402733…75440301380898652161
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
2.988 Γ— 10⁹⁷(98-digit number)
29888313248740805467…50880602761797304319
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:57,991,096 XPMΒ·at block #6,843,341 Β· updates every 60s
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