Block #447,070

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/17/2014, 12:32:55 AM · Difficulty 10.3597 · 6,380,168 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b398e23d76e57d3a15fe2c1f6fa6c7bc8293e2da13424dae702bd10b5dcf4b9d

View on Chainz ↗

Height

#447,070

Difficulty

10.359698

Transactions

Size

1003 B

Version

Bits

0a5c1523

Nonce

3,459

Timestamp

3/17/2014, 12:32:55 AM

Confirmations

6,380,168

Mined by

⛏️ ^aS&A+Aac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

af1220a0cb75f60394edf590cad18cdcb3a1a44252fdaeb9700287dad371ccae

Transactions (1)

Coinbaseaf1220a0cb75f6…0287dad371ccae

1 in → 25 out9.3000 XPM913 B

Aac9Hjdg…P4ktypc3 ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn AQ8QAT3J…rCFKuVbR AUnkFe8H…fvenjA4X

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.

2.599 × 10⁹⁴(95-digit number)

25998384641168061676…56497037273413722239

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

2.599 × 10⁹⁴(95-digit number)

25998384641168061676…56497037273413722239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.599 × 10⁹⁴(95-digit number)

25998384641168061676…56497037273413722241

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

5.199 × 10⁹⁴(95-digit number)

51996769282336123353…12994074546827444479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.199 × 10⁹⁴(95-digit number)

51996769282336123353…12994074546827444481

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

1.039 × 10⁹⁵(96-digit number)

10399353856467224670…25988149093654888959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.039 × 10⁹⁵(96-digit number)

10399353856467224670…25988149093654888961

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

2.079 × 10⁹⁵(96-digit number)

20798707712934449341…51976298187309777919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.079 × 10⁹⁵(96-digit number)

20798707712934449341…51976298187309777921

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

4.159 × 10⁹⁵(96-digit number)

41597415425868898683…03952596374619555839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.159 × 10⁹⁵(96-digit number)

41597415425868898683…03952596374619555841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #447,070

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