Block #147,478

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/3/2013, 3:23:54 AM · Difficulty 9.8519 · 6,646,832 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2471b1e468978d27371de6b19327a8eaa484ca95c649e72b1f9eea4197892865

View on Chainz ↗

Height

#147,478

Difficulty

9.851901

Transactions

Size

718 B

Version

Bits

09da1633

Nonce

142,232

Timestamp

9/3/2013, 3:23:54 AM

Confirmations

6,646,832

Merkle Root

33c4523d36e0d88ccafa306bf8eff1eea08e442c66568468c74623574a3188a7

Transactions (2)

Coinbasebe572db821ce3e…b390087382860f

1 in → 1 out10.3000 XPM109 B

AY3Rt1ex…GJoFTK6u

6be9ad97528bad…6673e34c2b6549

3 in → 2 out359.7593 XPM520 B

AW1MVK1w…2aFoEwhz AKUaiC3W…CLXsPPcd

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.

3.210 × 10⁹³(94-digit number)

32105698853762889633…84621588337962587139

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

3.210 × 10⁹³(94-digit number)

32105698853762889633…84621588337962587139

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.210 × 10⁹³(94-digit number)

32105698853762889633…84621588337962587141

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

6.421 × 10⁹³(94-digit number)

64211397707525779266…69243176675925174279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.421 × 10⁹³(94-digit number)

64211397707525779266…69243176675925174281

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

1.284 × 10⁹⁴(95-digit number)

12842279541505155853…38486353351850348559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.284 × 10⁹⁴(95-digit number)

12842279541505155853…38486353351850348561

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

2.568 × 10⁹⁴(95-digit number)

25684559083010311706…76972706703700697119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.568 × 10⁹⁴(95-digit number)

25684559083010311706…76972706703700697121

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

5.136 × 10⁹⁴(95-digit number)

51369118166020623412…53945413407401394239

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