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Block #3,341,338

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/5/2019, 12:49:09 AM Β· Difficulty 11.0029 Β· 3,501,451 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d1285c2b6edf3ad7396b411c64e3413ebbadb1686cdae627c2e793f50d530e1a
View on Chainz β†—

Height

#3,341,338

Difficulty

11.002903

Transactions

1

Size

202 B

Version

2

Bits

0b00be3e

Nonce

1,897,700,399

Timestamp

9/5/2019, 12:49:09 AM

Confirmations

3,501,451

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

63d08946c0a484d4c6c19b38069147b0f9deb6191e8c04ff35dcbc9c4defa948
Transactions (1)
Coinbase63d08946c0a484…dcbc9c4defa948
1 in β†’ 1 out8.2500 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.

5.741 Γ— 10⁹⁸(99-digit number)
57414650084887096912…76075523152343203839
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
5.741 Γ— 10⁹⁸(99-digit number)
57414650084887096912…76075523152343203839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.741 Γ— 10⁹⁸(99-digit number)
57414650084887096912…76075523152343203841
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
1.148 Γ— 10⁹⁹(100-digit number)
11482930016977419382…52151046304686407679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.148 Γ— 10⁹⁹(100-digit number)
11482930016977419382…52151046304686407681
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
2.296 Γ— 10⁹⁹(100-digit number)
22965860033954838765…04302092609372815359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.296 Γ— 10⁹⁹(100-digit number)
22965860033954838765…04302092609372815361
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
4.593 Γ— 10⁹⁹(100-digit number)
45931720067909677530…08604185218745630719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.593 Γ— 10⁹⁹(100-digit number)
45931720067909677530…08604185218745630721
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
9.186 Γ— 10⁹⁹(100-digit number)
91863440135819355060…17208370437491261439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.186 Γ— 10⁹⁹(100-digit number)
91863440135819355060…17208370437491261441
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
1.837 Γ— 10¹⁰⁰(101-digit number)
18372688027163871012…34416740874982522879
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:57,986,650 XPMΒ·at block #6,842,788 Β· updates every 60s
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