Block #372,932

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/23/2014, 10:55:28 PM · Difficulty 10.4276 · 6,453,543 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

463c4d76eb23e23ef93c33e679dd8baed8f36018a8e9a0ea6512be991b71f791

View on Chainz ↗

Height

#372,932

Difficulty

10.427592

Transactions

Size

829 B

Version

Bits

0a6d76a8

Nonce

33,558,231

Timestamp

1/23/2014, 10:55:28 PM

Confirmations

6,453,543

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

3bb3e1d886877c4ccaff0c903328b676dbfa2b1fd6f4567f0b45f2324a05daa4

Transactions (2)

Coinbase3284b35153c7f3…84b724477ec9c6

1 in → 1 out9.1900 XPM116 B

AbwWkWZt…kawDhufa

a51589229b875d…1626eb88dd8f3c

3 in → 8 out27.4400 XPM623 B

AT5q6oZQ…ZAxSXf5f AeKNrjNj…1NEq95Ta Abv8fCKK…5cEFFUzB APo8u8To…qebUkUEk AVrD6maY…W77cdqzz

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.

1.456 × 10⁹⁵(96-digit number)

14567284716345043184…61823807890927879119

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

1.456 × 10⁹⁵(96-digit number)

14567284716345043184…61823807890927879119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.456 × 10⁹⁵(96-digit number)

14567284716345043184…61823807890927879121

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

2.913 × 10⁹⁵(96-digit number)

29134569432690086369…23647615781855758239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.913 × 10⁹⁵(96-digit number)

29134569432690086369…23647615781855758241

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

5.826 × 10⁹⁵(96-digit number)

58269138865380172739…47295231563711516479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.826 × 10⁹⁵(96-digit number)

58269138865380172739…47295231563711516481

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

1.165 × 10⁹⁶(97-digit number)

11653827773076034547…94590463127423032959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.165 × 10⁹⁶(97-digit number)

11653827773076034547…94590463127423032961

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

2.330 × 10⁹⁶(97-digit number)

23307655546152069095…89180926254846065919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.330 × 10⁹⁶(97-digit number)

23307655546152069095…89180926254846065921

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 #372,932

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