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Block #3,325,406

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/24/2019, 7:08:42 PM Β· Difficulty 11.0202 Β· 3,515,513 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6b6b76863da4440dba5e317ceed1e5bce3ede3088f16b8ee5ddc2f08e46c3c26
View on Chainz β†—

Height

#3,325,406

Difficulty

11.020227

Transactions

2

Size

391 B

Version

2

Bits

0b052d92

Nonce

59,661,720

Timestamp

8/24/2019, 7:08:42 PM

Confirmations

3,515,513

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

b525c6b39096a4cf7b8d87659424255be730e50ebdff1cf521a719e42804021c
Transactions (2)
Coinbaseaf00e3f76bd366…244f9b149c9281
1 in β†’ 1 out8.2300 XPM110 B
ASiq2qtK…VMhmk7yL
fee0ddf7d639fe…a710db9c0ea7f4
1 in β†’ 1 out3.9900 XPM191 B
AeTHTL7A…vT1872bk
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.

5.309 Γ— 10⁹⁴(95-digit number)
53092347088174710427…32183402323246171519
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
5.309 Γ— 10⁹⁴(95-digit number)
53092347088174710427…32183402323246171519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.309 Γ— 10⁹⁴(95-digit number)
53092347088174710427…32183402323246171521
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
1.061 Γ— 10⁹⁡(96-digit number)
10618469417634942085…64366804646492343039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.061 Γ— 10⁹⁡(96-digit number)
10618469417634942085…64366804646492343041
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
2.123 Γ— 10⁹⁡(96-digit number)
21236938835269884171…28733609292984686079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.123 Γ— 10⁹⁡(96-digit number)
21236938835269884171…28733609292984686081
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
4.247 Γ— 10⁹⁡(96-digit number)
42473877670539768342…57467218585969372159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.247 Γ— 10⁹⁡(96-digit number)
42473877670539768342…57467218585969372161
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
8.494 Γ— 10⁹⁡(96-digit number)
84947755341079536684…14934437171938744319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.494 Γ— 10⁹⁡(96-digit number)
84947755341079536684…14934437171938744321
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
1.698 Γ— 10⁹⁢(97-digit number)
16989551068215907336…29868874343877488639
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:57,971,703 XPMΒ·at block #6,840,918 Β· updates every 60s
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