Block #148,939

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/4/2013, 1:27:36 AM · Difficulty 9.8561 · 6,643,291 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2ad6ac45c7c34695f15c1baba78fb1c2718e2b22b7c94e46764c9f51b17a7b24

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Height

#148,939

Difficulty

9.856105

Transactions

Size

199 B

Version

Bits

09db29b0

Nonce

142,257

Timestamp

9/4/2013, 1:27:36 AM

Confirmations

6,643,291

Merkle Root

012014009a07682ee909e65b51f828b224a6b090c9b07efdfd7465e355de3ba6

Transactions (1)

Coinbase012014009a0768…7465e355de3ba6

1 in → 1 out10.2800 XPM109 B

AcrXkx8M…tKGb6K4t

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.

2.017 × 10⁹⁵(96-digit number)

20179336400237430162…13790588226192323839

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

2.017 × 10⁹⁵(96-digit number)

20179336400237430162…13790588226192323839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.017 × 10⁹⁵(96-digit number)

20179336400237430162…13790588226192323841

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

4.035 × 10⁹⁵(96-digit number)

40358672800474860324…27581176452384647679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.035 × 10⁹⁵(96-digit number)

40358672800474860324…27581176452384647681

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

8.071 × 10⁹⁵(96-digit number)

80717345600949720648…55162352904769295359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.071 × 10⁹⁵(96-digit number)

80717345600949720648…55162352904769295361

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

1.614 × 10⁹⁶(97-digit number)

16143469120189944129…10324705809538590719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.614 × 10⁹⁶(97-digit number)

16143469120189944129…10324705809538590721

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

3.228 × 10⁹⁶(97-digit number)

32286938240379888259…20649411619077181439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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