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Block #3,951,639

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/15/2020, 10:26:14 PM Β· Difficulty 10.8763 Β· 2,891,294 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1833946c7d3e9d280c2b00d390519b11b606ef850e77efc6ce2d43da10e3f394
View on Chainz β†—

Height

#3,951,639

Difficulty

10.876343

Transactions

2

Size

1.72 KB

Version

2

Bits

0ae05801

Nonce

954,329,300

Timestamp

11/15/2020, 10:26:14 PM

Confirmations

2,891,294

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

415833bf2a2060383e144f88dab0805ff3d5092904950f7341793db7192a4793
Transactions (2)
Coinbase151ca71f29ac0b…f1964a8d90787e
1 in β†’ 1 out8.4600 XPM110 B
ASiq2qtK…VMhmk7yL
872828b3b5cab1…f7553f6cbc9ac1
10 in β†’ 2 out10018.4921 XPM1.52 KB
ALgPw6re…xzH9ZzQGAa6Ft23G…2f6sWqaF
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.

3.529 Γ— 10⁹⁴(95-digit number)
35290534293342724617…49849484334351918079
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
3.529 Γ— 10⁹⁴(95-digit number)
35290534293342724617…49849484334351918079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.529 Γ— 10⁹⁴(95-digit number)
35290534293342724617…49849484334351918081
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
7.058 Γ— 10⁹⁴(95-digit number)
70581068586685449234…99698968668703836159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.058 Γ— 10⁹⁴(95-digit number)
70581068586685449234…99698968668703836161
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
1.411 Γ— 10⁹⁡(96-digit number)
14116213717337089846…99397937337407672319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.411 Γ— 10⁹⁡(96-digit number)
14116213717337089846…99397937337407672321
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
2.823 Γ— 10⁹⁡(96-digit number)
28232427434674179693…98795874674815344639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.823 Γ— 10⁹⁡(96-digit number)
28232427434674179693…98795874674815344641
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
5.646 Γ— 10⁹⁡(96-digit number)
56464854869348359387…97591749349630689279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.646 Γ— 10⁹⁡(96-digit number)
56464854869348359387…97591749349630689281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,987,813 XPMΒ·at block #6,842,932 Β· updates every 60s
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