Block #2,978,728

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/23/2018, 9:30:52 PM · Difficulty 11.2897 · 3,852,731 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ed84d3c38e3433f18487a0224113999fe35bb10f563388374bb0e7717e348a15

View on Chainz ↗

Height

#2,978,728

Difficulty

11.289691

Transactions

Size

1.89 KB

Version

Bits

0b4a292a

Nonce

39,959,870

Timestamp

12/23/2018, 9:30:52 PM

Confirmations

3,852,731

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

e6c25ccbb9210e4485b24ff1244eccc2119c45369b65dbb76d7f8a6f9831ea96

Transactions (2)

Coinbase83496a2f9e470a…bb5c14fe3d276d

1 in → 1 out7.8800 XPM110 B

AUMQRepm…tAfKmdW1

5d8ec7ae1700b6…d814db49da9a54

11 in → 3 out13265.1139 XPM1.70 KB

ARywRRZa…HVd3P31R AbfHPQRP…cc1QCTYa AZ4dYmPD…1J5q5fF4

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.

4.861 × 10⁹⁷(98-digit number)

48618283095021931607…96566341528951521279

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

4.861 × 10⁹⁷(98-digit number)

48618283095021931607…96566341528951521279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.861 × 10⁹⁷(98-digit number)

48618283095021931607…96566341528951521281

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

9.723 × 10⁹⁷(98-digit number)

97236566190043863215…93132683057903042559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.723 × 10⁹⁷(98-digit number)

97236566190043863215…93132683057903042561

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

1.944 × 10⁹⁸(99-digit number)

19447313238008772643…86265366115806085119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.944 × 10⁹⁸(99-digit number)

19447313238008772643…86265366115806085121

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

3.889 × 10⁹⁸(99-digit number)

38894626476017545286…72530732231612170239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.889 × 10⁹⁸(99-digit number)

38894626476017545286…72530732231612170241

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

7.778 × 10⁹⁸(99-digit number)

77789252952035090572…45061464463224340479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.778 × 10⁹⁸(99-digit number)

77789252952035090572…45061464463224340481

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

1.555 × 10⁹⁹(100-digit number)

15557850590407018114…90122928926448680959

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 #2,978,728

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