Block #2,643,138

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/1/2018, 11:57:36 PM · Difficulty 11.6749 · 4,201,600 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

26d16839dfdd7c4123a9189c9185d8c4813162702025865be2f90c95c8a020ba

View on Chainz ↗

Height

#2,643,138

Difficulty

11.674882

Transactions

Size

1.37 KB

Version

Bits

0bacc509

Nonce

381,517,425

Timestamp

5/1/2018, 11:57:36 PM

Confirmations

4,201,600

Mined by

⛏️ P2SHANMqMtWNFMyErpW6CKTYoN4S4nGEm1QRaX

Merkle Root

4583c2d5525597459d032b452060e8a3a4e523809f688755f0a29227ac7b85f4

Transactions (5)

Coinbaseda498a5adbd1bb…19a2e00b382b22

1 in → 1 out7.3600 XPM110 B

ANMqMtWN…GEm1QRaX

b8abb656034bf2…e149afa1a9c2f9

1 in → 2 out268517.3155 XPM226 B

AR6Ns8MQ…SAim9Z1X AStgCJcF…akjrqFXV

dc1fe409cd7073…4dbacfc10c3d28

1 in → 2 out4.3240 XPM227 B

AMQodXvZ…5v3YbTPH AZBGBBQd…ExqEYGNc

605a87c6498b27…b044c4fd355ae2

1 in → 2 out3.3359 XPM226 B

ATXigEzd…ZHk4Tsrg AZBGBBQd…ExqEYGNc

2e3139457b7692…0780f6ab07d4d0

3 in → 2 out0.5430 XPM524 B

AGSgK9dx…788YqK8p AVcFpc7n…KyxRTppr

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.770 × 10⁹⁹(100-digit number)

37703807225211196926…23462861326828175359

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

3.770 × 10⁹⁹(100-digit number)

37703807225211196926…23462861326828175359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.770 × 10⁹⁹(100-digit number)

37703807225211196926…23462861326828175361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

7.540 × 10⁹⁹(100-digit number)

75407614450422393852…46925722653656350719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.540 × 10⁹⁹(100-digit number)

75407614450422393852…46925722653656350721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.508 × 10¹⁰⁰(101-digit number)

15081522890084478770…93851445307312701439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.508 × 10¹⁰⁰(101-digit number)

15081522890084478770…93851445307312701441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

3.016 × 10¹⁰⁰(101-digit number)

30163045780168957540…87702890614625402879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.016 × 10¹⁰⁰(101-digit number)

30163045780168957540…87702890614625402881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

6.032 × 10¹⁰⁰(101-digit number)

60326091560337915081…75405781229250805759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.032 × 10¹⁰⁰(101-digit number)

60326091560337915081…75405781229250805761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.206 × 10¹⁰¹(102-digit number)

12065218312067583016…50811562458501611519

Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #2,643,138

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