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Block #2,819,102

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/31/2018, 11:07:04 PM Β· Difficulty 11.7013 Β· 4,017,803 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
95845eb3b51f87055a0c73d9839f32f72fdcd78f85e4a79cb5ad2423fad44d8b
View on Chainz β†—

Height

#2,819,102

Difficulty

11.701289

Transactions

1

Size

202 B

Version

2

Bits

0bb387b0

Nonce

161,824,273

Timestamp

8/31/2018, 11:07:04 PM

Confirmations

4,017,803

Mined by

⛏️ P2SHAK13qv5cm9iRTDJWXqnxDjM9T7fukfcoay

Merkle Root

64b3a177f2075f85bcf6de08edf5e84906298e866b05807e443a8d99f78abbcf
Transactions (1)
Coinbase64b3a177f2075f…3a8d99f78abbcf
1 in β†’ 1 out7.2900 XPM110 B
AK13qv5c…fukfcoay
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.

4.605 Γ— 10⁹⁹(100-digit number)
46052630003575848990…08957314725639618559
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
4.605 Γ— 10⁹⁹(100-digit number)
46052630003575848990…08957314725639618559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.605 Γ— 10⁹⁹(100-digit number)
46052630003575848990…08957314725639618561
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
9.210 Γ— 10⁹⁹(100-digit number)
92105260007151697980…17914629451279237119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.210 Γ— 10⁹⁹(100-digit number)
92105260007151697980…17914629451279237121
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
1.842 Γ— 10¹⁰⁰(101-digit number)
18421052001430339596…35829258902558474239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.842 Γ— 10¹⁰⁰(101-digit number)
18421052001430339596…35829258902558474241
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
3.684 Γ— 10¹⁰⁰(101-digit number)
36842104002860679192…71658517805116948479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.684 Γ— 10¹⁰⁰(101-digit number)
36842104002860679192…71658517805116948481
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
7.368 Γ— 10¹⁰⁰(101-digit number)
73684208005721358384…43317035610233896959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.368 Γ— 10¹⁰⁰(101-digit number)
73684208005721358384…43317035610233896961
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
1.473 Γ— 10¹⁰¹(102-digit number)
14736841601144271676…86634071220467793919
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:57,939,532 XPMΒ·at block #6,836,904 Β· updates every 60s
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