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Block #2,826,940

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/6/2018, 7:18:57 AM Β· Difficulty 11.7100 Β· 4,015,395 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dc2d5706b03531ca566689497c11bf818cd37f785f31e1fe06e90d14858b9d50
View on Chainz β†—

Height

#2,826,940

Difficulty

11.710043

Transactions

1

Size

201 B

Version

2

Bits

0bb5c569

Nonce

876,712,216

Timestamp

9/6/2018, 7:18:57 AM

Confirmations

4,015,395

Mined by

⛏️ P2SHAVaAFaMts6cJs4qDrLppUrEoWrGnkr6oMQ

Merkle Root

bb0fa38e4c605bcb3ded20e1c92d5d0283f3fad36b88050409ba2e053fd0fa97
Transactions (1)
Coinbasebb0fa38e4c605b…ba2e053fd0fa97
1 in β†’ 1 out7.2800 XPM110 B
AVaAFaMt…Gnkr6oMQ
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.

3.776 Γ— 10⁹⁷(98-digit number)
37763737737268384546…02325351514832240639
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
3.776 Γ— 10⁹⁷(98-digit number)
37763737737268384546…02325351514832240639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.776 Γ— 10⁹⁷(98-digit number)
37763737737268384546…02325351514832240641
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
7.552 Γ— 10⁹⁷(98-digit number)
75527475474536769093…04650703029664481279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.552 Γ— 10⁹⁷(98-digit number)
75527475474536769093…04650703029664481281
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
1.510 Γ— 10⁹⁸(99-digit number)
15105495094907353818…09301406059328962559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.510 Γ— 10⁹⁸(99-digit number)
15105495094907353818…09301406059328962561
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
3.021 Γ— 10⁹⁸(99-digit number)
30210990189814707637…18602812118657925119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.021 Γ— 10⁹⁸(99-digit number)
30210990189814707637…18602812118657925121
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
6.042 Γ— 10⁹⁸(99-digit number)
60421980379629415274…37205624237315850239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.042 Γ— 10⁹⁸(99-digit number)
60421980379629415274…37205624237315850241
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
1.208 Γ— 10⁹⁹(100-digit number)
12084396075925883054…74411248474631700479
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:57,983,086 XPMΒ·at block #6,842,334 Β· updates every 60s
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