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Block #3,082,784

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/7/2019, 5:47:04 PM Β· Difficulty 11.0226 Β· 3,755,318 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dd1b5edce3c8d15632f1ff9df25e7d2222e84463cef8cd093267022e7f8ae9f0
View on Chainz β†—

Height

#3,082,784

Difficulty

11.022647

Transactions

2

Size

573 B

Version

2

Bits

0b05cc2a

Nonce

582,650,513

Timestamp

3/7/2019, 5:47:04 PM

Confirmations

3,755,318

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

86497e99496dd4857b917f2c250943bd31114f8ef7fa84e77e9b1c7f70eeab4d
Transactions (2)
Coinbaseb91f4ffb737347…a0b98e90769a34
1 in β†’ 1 out8.2300 XPM110 B
AbXwmGxD…4XXYP765
c457ec97e7b425…5d3d423b38a531
2 in β†’ 2 out281.0929 XPM373 B
AeTHTL7A…vT1872bkAPMuYwUx…bRc4gMeh
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.

2.060 Γ— 10⁹⁴(95-digit number)
20604061494814501053…80123788397161923039
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
2.060 Γ— 10⁹⁴(95-digit number)
20604061494814501053…80123788397161923039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.060 Γ— 10⁹⁴(95-digit number)
20604061494814501053…80123788397161923041
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
4.120 Γ— 10⁹⁴(95-digit number)
41208122989629002107…60247576794323846079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.120 Γ— 10⁹⁴(95-digit number)
41208122989629002107…60247576794323846081
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
8.241 Γ— 10⁹⁴(95-digit number)
82416245979258004214…20495153588647692159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.241 Γ— 10⁹⁴(95-digit number)
82416245979258004214…20495153588647692161
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
1.648 Γ— 10⁹⁡(96-digit number)
16483249195851600842…40990307177295384319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.648 Γ— 10⁹⁡(96-digit number)
16483249195851600842…40990307177295384321
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
3.296 Γ— 10⁹⁡(96-digit number)
32966498391703201685…81980614354590768639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.296 Γ— 10⁹⁡(96-digit number)
32966498391703201685…81980614354590768641
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
6.593 Γ— 10⁹⁡(96-digit number)
65932996783406403371…63961228709181537279
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:57,949,169 XPMΒ·at block #6,838,101 Β· updates every 60s
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