Block #224,970

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/24/2013, 3:50:05 AM · Difficulty 9.9368 · 6,585,318 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a25ec3faf72b8ca26db7a14cacef86e5a82dfe1b61431c94b2b79694b9245023

View on Chainz ↗

Height

#224,970

Difficulty

9.936849

Transactions

Size

800 B

Version

Bits

09efd556

Nonce

53,553

Timestamp

10/24/2013, 3:50:05 AM

Confirmations

6,585,318

Mined by

⛏️ P2SHAGEoPbWnmbbW3kPqNu4vz42znk6ptPib5T

Merkle Root

f754eca37622c87adc26f70c34f25254efa837cde768a315974219a463e7b080

Transactions (3)

Coinbasef6e254787a13c8…a42d2545df0be1

1 in → 1 out10.1300 XPM109 B

AGEoPbWn…6ptPib5T

419d6d709b6af3…f37e538e86a890

2 in → 2 out20.2100 XPM375 B

AZKDCx6Z…78t8s9LZ AemanUAC…tZBjddPH

95ac5f20bdc4f2…b1fed33f30d493

1 in → 2 out10.1000 XPM226 B

AP5HdXuK…sHJ1rnze AeTde7fH…w7crTzqr

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.

4.415 × 10⁹⁴(95-digit number)

44152611410965612788…19993172143187770239

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

4.415 × 10⁹⁴(95-digit number)

44152611410965612788…19993172143187770239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.415 × 10⁹⁴(95-digit number)

44152611410965612788…19993172143187770241

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

8.830 × 10⁹⁴(95-digit number)

88305222821931225576…39986344286375540479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.830 × 10⁹⁴(95-digit number)

88305222821931225576…39986344286375540481

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

1.766 × 10⁹⁵(96-digit number)

17661044564386245115…79972688572751080959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.766 × 10⁹⁵(96-digit number)

17661044564386245115…79972688572751080961

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

3.532 × 10⁹⁵(96-digit number)

35322089128772490230…59945377145502161919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.532 × 10⁹⁵(96-digit number)

35322089128772490230…59945377145502161921

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

7.064 × 10⁹⁵(96-digit number)

70644178257544980460…19890754291004323839

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

Block #224,970

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