Block #148,934

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/4/2013, 1:19:53 AM · Difficulty 9.8562 · 6,656,135 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

55699e2cd05ba4d6e0370fd9c49f5a20e6ace57982d0db4b12384a9722f4d6e2

View on Chainz ↗

Height

#148,934

Difficulty

9.856160

Transactions

Size

198 B

Version

Bits

09db2d4b

Nonce

89,981

Timestamp

9/4/2013, 1:19:53 AM

Confirmations

6,656,135

Mined by

⛏️ P2SHAJkcBGvuouoWiEQ4AmFvGo3qwPhSNwhPED

Merkle Root

864951395f15b95ddac23a7f951dd0056cfe297b50e7ae15fecd6b619a9f2f88

Transactions (1)

Coinbase864951395f15b9…cd6b619a9f2f88

1 in → 1 out10.2800 XPM109 B

AJkcBGvu…hSNwhPED

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.

1.821 × 10⁹²(93-digit number)

18210535090152903253…56925399770919496999

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

1.821 × 10⁹²(93-digit number)

18210535090152903253…56925399770919496999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.821 × 10⁹²(93-digit number)

18210535090152903253…56925399770919497001

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

3.642 × 10⁹²(93-digit number)

36421070180305806507…13850799541838993999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.642 × 10⁹²(93-digit number)

36421070180305806507…13850799541838994001

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

7.284 × 10⁹²(93-digit number)

72842140360611613015…27701599083677987999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.284 × 10⁹²(93-digit number)

72842140360611613015…27701599083677988001

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

1.456 × 10⁹³(94-digit number)

14568428072122322603…55403198167355975999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.456 × 10⁹³(94-digit number)

14568428072122322603…55403198167355976001

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

2.913 × 10⁹³(94-digit number)

29136856144244645206…10806396334711951999

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