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Block #3,432,633

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/14/2019, 9:36:31 AM Β· Difficulty 10.9800 Β· 3,394,522 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3e9d4dda9298c839646ba1394edba97089df7e05a4adffdaa6d56a16df22f6c3
View on Chainz β†—

Height

#3,432,633

Difficulty

10.980010

Transactions

1

Size

200 B

Version

2

Bits

0afae1f5

Nonce

280,033,923

Timestamp

11/14/2019, 9:36:31 AM

Confirmations

3,394,522

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

5c9de59cb64997240fcb582efacb506e293d9fcf6b2d24b7eb2ed8345a93b10e
Transactions (1)
Coinbase5c9de59cb64997…2ed8345a93b10e
1 in β†’ 1 out8.2800 XPM110 B
ASiq2qtK…VMhmk7yL
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.

2.942 Γ— 10⁹⁴(95-digit number)
29421549626417304999…17531301727271144039
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
2.942 Γ— 10⁹⁴(95-digit number)
29421549626417304999…17531301727271144039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.942 Γ— 10⁹⁴(95-digit number)
29421549626417304999…17531301727271144041
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
5.884 Γ— 10⁹⁴(95-digit number)
58843099252834609998…35062603454542288079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.884 Γ— 10⁹⁴(95-digit number)
58843099252834609998…35062603454542288081
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
1.176 Γ— 10⁹⁡(96-digit number)
11768619850566921999…70125206909084576159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.176 Γ— 10⁹⁡(96-digit number)
11768619850566921999…70125206909084576161
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
2.353 Γ— 10⁹⁡(96-digit number)
23537239701133843999…40250413818169152319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.353 Γ— 10⁹⁡(96-digit number)
23537239701133843999…40250413818169152321
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
4.707 Γ— 10⁹⁡(96-digit number)
47074479402267687999…80500827636338304639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.707 Γ— 10⁹⁡(96-digit number)
47074479402267687999…80500827636338304641
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:57,861,424 XPMΒ·at block #6,827,154 Β· updates every 60s
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