Block #154,952

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/8/2013, 12:25:27 AM · Difficulty 9.8651 · 6,648,661 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d6eac9591b2b7726b3f49eb9905cb700fab88219c29dec48e9e8b1c07cd71cee

View on Chainz ↗

Height

#154,952

Difficulty

9.865079

Transactions

Size

1.07 KB

Version

Bits

09dd75d9

Nonce

12,540

Timestamp

9/8/2013, 12:25:27 AM

Confirmations

6,648,661

Mined by

⛏️ P2SHAWN2MUgSRxa1WJ5mDETpZmTiz6zCBa8z22

Merkle Root

601450c104ef4706564790c2df0711e238758e5dbf77dd23395b5154797f1a2c

Transactions (3)

Coinbase6637227b59e02a…eb8b48a8824e12

1 in → 1 out10.2800 XPM109 B

AWN2MUgS…zCBa8z22

3953c720dddbeb…c661c4cbf1b42e

1 in → 2 out5.2124 XPM226 B

AcN7Mwej…Rnr1man2 AQcqxrnd…1uxvq9hA

e5f686e14cd7bb…be8fd1c3519133

4 in → 2 out10.0849 XPM667 B

AX5ePwBj…KQZQXguc AMfKk4b8…16WysXxn

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.

6.959 × 10⁹⁵(96-digit number)

69594472313345111703…19130704875561885919

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

6.959 × 10⁹⁵(96-digit number)

69594472313345111703…19130704875561885919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.959 × 10⁹⁵(96-digit number)

69594472313345111703…19130704875561885921

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

1.391 × 10⁹⁶(97-digit number)

13918894462669022340…38261409751123771839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.391 × 10⁹⁶(97-digit number)

13918894462669022340…38261409751123771841

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

2.783 × 10⁹⁶(97-digit number)

27837788925338044681…76522819502247543679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.783 × 10⁹⁶(97-digit number)

27837788925338044681…76522819502247543681

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

5.567 × 10⁹⁶(97-digit number)

55675577850676089362…53045639004495087359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.567 × 10⁹⁶(97-digit number)

55675577850676089362…53045639004495087361

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

1.113 × 10⁹⁷(98-digit number)

11135115570135217872…06091278008990174719

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