Block #2,740,522

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 7/9/2018, 4:25:07 AM · Difficulty 11.6225 · 4,101,142 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8a63d54331073efca54e6660a9fbcc65942b03af9909680cda00f6a3a9bfd6db

View on Chainz ↗

Height

#2,740,522

Difficulty

11.622548

Transactions

Size

1.96 KB

Version

Bits

0b9f5f4c

Nonce

23,994,266

Timestamp

7/9/2018, 4:25:07 AM

Confirmations

4,101,142

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

5482b8556f853db265e2761bb59bd1bcb051c0de927d3aa76fb8a4b974e3c4ff

Transactions (5)

Coinbase3e06f068e028f3…915b84cf5a425a

1 in → 1 out7.4300 XPM110 B

AZtxQr2F…7grUWrUz

6045a45ed38686…41381c69fee612

3 in → 2 out20.2005 XPM455 B

AKTvTS2o…nBJ4H6PJ AWu6SVKR…fD2XKYmk

4cd04c16904448…795eda3ad55246

2 in → 2 out13.7991 XPM338 B

AYnThcdb…teYxBFmA AZf9Bapn…tj8yz1b6

c0170700a2f818…4449481fe41330

5 in → 2 out10.0459 XPM784 B

AQVREjJu…KrvuQ8kf AeFPzsec…hFVYg7Ng

e198f093f47f69…1623f778e092fe

1 in → 2 out6.8849 XPM226 B

ATn81mmA…CpgVU9ud AGbm9W17…Jvw6eg2t

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.

3.451 × 10⁹⁴(95-digit number)

34510106926950715985…64619249431426430639

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

3.451 × 10⁹⁴(95-digit number)

34510106926950715985…64619249431426430639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.451 × 10⁹⁴(95-digit number)

34510106926950715985…64619249431426430641

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

6.902 × 10⁹⁴(95-digit number)

69020213853901431970…29238498862852861279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.902 × 10⁹⁴(95-digit number)

69020213853901431970…29238498862852861281

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

1.380 × 10⁹⁵(96-digit number)

13804042770780286394…58476997725705722559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.380 × 10⁹⁵(96-digit number)

13804042770780286394…58476997725705722561

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

2.760 × 10⁹⁵(96-digit number)

27608085541560572788…16953995451411445119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.760 × 10⁹⁵(96-digit number)

27608085541560572788…16953995451411445121

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

5.521 × 10⁹⁵(96-digit number)

55216171083121145576…33907990902822890239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.521 × 10⁹⁵(96-digit number)

55216171083121145576…33907990902822890241

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

1.104 × 10⁹⁶(97-digit number)

11043234216624229115…67815981805645780479

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

1.104 × 10⁹⁶(97-digit number)

11043234216624229115…67815981805645780481

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 #2,740,522

Cookie Preferences