Block #378,386

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/27/2014, 7:07:10 PM · Difficulty 10.4203 · 6,430,705 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3642268af5649484b55e475dbc39646094796c37e37294f9b56b3e86310635ba

View on Chainz ↗

Height

#378,386

Difficulty

10.420284

Transactions

Size

878 B

Version

Bits

0a6b97be

Nonce

153,731

Timestamp

1/27/2014, 7:07:10 PM

Confirmations

6,430,705

Mined by

⛏️ P2SHAWQ3mouGbYquwYE2vprTzb1jVNHp6Pb56R

Merkle Root

f8ae6ff5f619c47d26dc71b0430f121dc666ff037ab82c7bdfcf42f804cd1658

Transactions (4)

Coinbase9f8dff0cefaaeb…92e8b7249dd27f

1 in → 1 out9.2300 XPM109 B

AWQ3mouG…Hp6Pb56R

1b39634116f8aa…c0684dabf53138

1 in → 2 out8.1694 XPM226 B

AbKUwSy7…kJFB3ajq ALQx59LV…R8LoHHSH

f597a6be5250cb…e5bbb4010cc6ad

1 in → 2 out7.1534 XPM226 B

ATapjzLj…XR2tNS2f AZC6eNvq…viRp2Arm

ede73268f85b7d…1cd42135a3c6da

1 in → 2 out2.0285 XPM227 B

AJcsqbCd…WonMqpwC ATAKPxfU…UDFQSaUH

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.

3.591 × 10⁹⁵(96-digit number)

35916994730793144236…65755791395143234199

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

3.591 × 10⁹⁵(96-digit number)

35916994730793144236…65755791395143234199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.591 × 10⁹⁵(96-digit number)

35916994730793144236…65755791395143234201

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

7.183 × 10⁹⁵(96-digit number)

71833989461586288473…31511582790286468399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.183 × 10⁹⁵(96-digit number)

71833989461586288473…31511582790286468401

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

1.436 × 10⁹⁶(97-digit number)

14366797892317257694…63023165580572936799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.436 × 10⁹⁶(97-digit number)

14366797892317257694…63023165580572936801

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

2.873 × 10⁹⁶(97-digit number)

28733595784634515389…26046331161145873599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.873 × 10⁹⁶(97-digit number)

28733595784634515389…26046331161145873601

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

5.746 × 10⁹⁶(97-digit number)

57467191569269030778…52092662322291747199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.746 × 10⁹⁶(97-digit number)

57467191569269030778…52092662322291747201

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 #378,386

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