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Block #2,646,325

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/3/2018, 7:37:00 AM Β· Difficulty 11.7482 Β· 4,184,252 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1351ebfac1041b7cc109108b12986710ebb91c65ef50b5674df9f41529b0b10f
View on Chainz β†—

Height

#2,646,325

Difficulty

11.748248

Transactions

2

Size

1.14 KB

Version

2

Bits

0bbf8d2f

Nonce

1,885,598,798

Timestamp

5/3/2018, 7:37:00 AM

Confirmations

4,184,252

Mined by

⛏️ P2SHAMxvK8mKSTBtp43767RmFwB66Ce91khqze

Merkle Root

69116e86afcda1c4b1dc4a14c2799be89021d2332b29c738029480e1e004361b
Transactions (2)
Coinbasefa54b1b80aa2cf…625a295f3eec27
1 in β†’ 1 out7.2400 XPM110 B
AMxvK8mK…e91khqze
af904e9976b7d2…1c1f514ad3deb8
6 in β†’ 2 out14.9809 XPM968 B
APhUPPN6…Z3BJ2ukuAUMAFvFG…U3tviQiX
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.

3.272 Γ— 10⁹⁴(95-digit number)
32721343712190898453…20370851290845467839
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
3.272 Γ— 10⁹⁴(95-digit number)
32721343712190898453…20370851290845467839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.272 Γ— 10⁹⁴(95-digit number)
32721343712190898453…20370851290845467841
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
6.544 Γ— 10⁹⁴(95-digit number)
65442687424381796906…40741702581690935679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.544 Γ— 10⁹⁴(95-digit number)
65442687424381796906…40741702581690935681
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
1.308 Γ— 10⁹⁡(96-digit number)
13088537484876359381…81483405163381871359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.308 Γ— 10⁹⁡(96-digit number)
13088537484876359381…81483405163381871361
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
2.617 Γ— 10⁹⁡(96-digit number)
26177074969752718762…62966810326763742719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.617 Γ— 10⁹⁡(96-digit number)
26177074969752718762…62966810326763742721
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
5.235 Γ— 10⁹⁡(96-digit number)
52354149939505437525…25933620653527485439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.235 Γ— 10⁹⁡(96-digit number)
52354149939505437525…25933620653527485441
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
1.047 Γ— 10⁹⁢(97-digit number)
10470829987901087505…51867241307054970879
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:57,888,746 XPMΒ·at block #6,830,576 Β· updates every 60s
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