Block #151,393

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/5/2013, 3:56:18 PM · Difficulty 9.8603 · 6,653,654 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5b91ca6d4d0d855743817c098dd77421ea537c7ce41ef03e19a98e564fd93630

View on Chainz ↗

Height

#151,393

Difficulty

9.860315

Transactions

Size

1.64 KB

Version

Bits

09dc3d9b

Nonce

98,724

Timestamp

9/5/2013, 3:56:18 PM

Confirmations

6,653,654

Mined by

⛏️ P2SHAaEaYYnPHwN5nsaWg4Ph9o3KviGEYib9go

Merkle Root

b4b00c78d5fb073178bf6d6501536c29b81b67dd50b64d6198f0438c4ebb5109

Transactions (2)

Coinbased5286e7de65bd5…4cbe8913662125

1 in → 1 out10.2900 XPM109 B

AaEaYYnP…GEYib9go

bcda17c796d64d…7a95fc9ff21268

12 in → 2 out119.7000 XPM1.44 KB

ASoxTfVQ…vCvp58L6 AGZvBxxa…shhkwtTn

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.

7.937 × 10⁹⁵(96-digit number)

79379998148186976232…82896252911908843839

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

7.937 × 10⁹⁵(96-digit number)

79379998148186976232…82896252911908843839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.937 × 10⁹⁵(96-digit number)

79379998148186976232…82896252911908843841

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

1.587 × 10⁹⁶(97-digit number)

15875999629637395246…65792505823817687679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.587 × 10⁹⁶(97-digit number)

15875999629637395246…65792505823817687681

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

3.175 × 10⁹⁶(97-digit number)

31751999259274790493…31585011647635375359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.175 × 10⁹⁶(97-digit number)

31751999259274790493…31585011647635375361

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

6.350 × 10⁹⁶(97-digit number)

63503998518549580986…63170023295270750719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.350 × 10⁹⁶(97-digit number)

63503998518549580986…63170023295270750721

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

1.270 × 10⁹⁷(98-digit number)

12700799703709916197…26340046590541501439

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