Block #446,581

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/16/2014, 4:18:49 PM · Difficulty 10.3596 · 6,348,293 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ccbcf80486bb56c728660b290261ff0f98e2ccd419eaf85858feb4c490da3261

View on Chainz ↗

Height

#446,581

Difficulty

10.359607

Transactions

Size

425 B

Version

Bits

0a5c0f3b

Nonce

20,046,498

Timestamp

3/16/2014, 4:18:49 PM

Confirmations

6,348,293

Mined by

⛏️ P2SHAREbHfLGtCnt1on8464STKJRqaHzcHGNAE

Merkle Root

e0e353a9eb9b477df56d3704d72a20a2f883dcdbf4e69c659c1f19ad72d20dce

Transactions (2)

Coinbase4252d2f02bf042…1d67b20a5bc4b5

1 in → 1 out9.3100 XPM109 B

AREbHfLG…HzcHGNAE

d6ae210a1cbe54…5d58120065f53e

1 in → 2 out10.0100 XPM226 B

ALPhoXEV…ikaBivTY Aatv2skd…5gMmqvZp

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.

2.912 × 10⁹⁵(96-digit number)

29128715973205897389…75430199938269492799

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

2.912 × 10⁹⁵(96-digit number)

29128715973205897389…75430199938269492799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.912 × 10⁹⁵(96-digit number)

29128715973205897389…75430199938269492801

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

5.825 × 10⁹⁵(96-digit number)

58257431946411794778…50860399876538985599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.825 × 10⁹⁵(96-digit number)

58257431946411794778…50860399876538985601

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

1.165 × 10⁹⁶(97-digit number)

11651486389282358955…01720799753077971199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.165 × 10⁹⁶(97-digit number)

11651486389282358955…01720799753077971201

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

2.330 × 10⁹⁶(97-digit number)

23302972778564717911…03441599506155942399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.330 × 10⁹⁶(97-digit number)

23302972778564717911…03441599506155942401

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

4.660 × 10⁹⁶(97-digit number)

46605945557129435822…06883199012311884799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.660 × 10⁹⁶(97-digit number)

46605945557129435822…06883199012311884801

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