Block #433,869

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/7/2014, 9:07:40 PM · Difficulty 10.3471 · 6,382,697 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0bf2216fd0cf0f6717ec7f19b258f73c97d55fc32e369c9ac8a2628fc715ebb8

View on Chainz ↗

Height

#433,869

Difficulty

10.347127

Transactions

Size

1.46 KB

Version

Bits

0a58dd57

Nonce

241

Timestamp

3/7/2014, 9:07:40 PM

Confirmations

6,382,697

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

1750f87368775172f64a8318d6cbae7051d9a2225942d349d351dc7519e77e76

Transactions (3)

Coinbasea96c92ac0ba5b6…c18700dfd97368

1 in → 1 out9.3500 XPM110 B

AeKNrjNj…1NEq95Ta

95bc45e873f89f…75f1e9a058fe71

5 in → 2 out33.7975 XPM818 B

Ab4EpWsv…MD5PbBcL AbEfq5hq…Rce9jnqv

aa0e12c26ffcb8…abc40f30e98c4f

2 in → 7 out18.6500 XPM478 B

AMf8PhfM…AME5WSpE AHy24nCY…4KpVC1Hz ANyubE6h…EukxTvhy AWpvCBBf…yE35vgWj AeKNrjNj…1NEq95Ta

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.

3.786 × 10⁹⁴(95-digit number)

37860754242402254664…36589136163846470399

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

3.786 × 10⁹⁴(95-digit number)

37860754242402254664…36589136163846470399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.786 × 10⁹⁴(95-digit number)

37860754242402254664…36589136163846470401

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

7.572 × 10⁹⁴(95-digit number)

75721508484804509329…73178272327692940799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.572 × 10⁹⁴(95-digit number)

75721508484804509329…73178272327692940801

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

1.514 × 10⁹⁵(96-digit number)

15144301696960901865…46356544655385881599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.514 × 10⁹⁵(96-digit number)

15144301696960901865…46356544655385881601

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

3.028 × 10⁹⁵(96-digit number)

30288603393921803731…92713089310771763199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.028 × 10⁹⁵(96-digit number)

30288603393921803731…92713089310771763201

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

6.057 × 10⁹⁵(96-digit number)

60577206787843607463…85426178621543526399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.057 × 10⁹⁵(96-digit number)

60577206787843607463…85426178621543526401

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 #433,869

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