Block #380,542

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/29/2014, 8:15:26 AM · Difficulty 10.4124 · 6,427,355 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

99b20c1f8080a8583dffe45fe12526f857639bc293acd079792b0cbcb5dbcde4

View on Chainz ↗

Height

#380,542

Difficulty

10.412380

Transactions

Size

28.56 KB

Version

Bits

0a6991b8

Nonce

35,338

Timestamp

1/29/2014, 8:15:26 AM

Confirmations

6,427,355

Mined by

⛏️ P2SHAMYxaAVZAsuuRbFXxaYZRqLx2RNVJuWoFH

Merkle Root

105b68ccd96e1c6eb7bb90e55e54e98805658d9d7fd2e8a88de9c9e3f0ebf8a3

Transactions (3)

Coinbaseb339088ea02751…15d8ef7f4ac834

1 in → 1 out9.5100 XPM109 B

AMYxaAVZ…NVJuWoFH

f074fc1430c4c9…68248d4ed74cbf

2 in → 6 out18.9813 XPM444 B

ARvDQa73…HKBPbEPw AHx6AsKJ…1ijLBcnE ASTcaxJ4…gURy1LJz AMurAYrb…3iomaSF2 AY7Pf4bp…zHUNyeEi

a80e6f104dd983…6fd03134327958

193 in → 1 out67.1874 XPM27.93 KB

AXbC4y6F…B2HknvKz

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.

4.638 × 10¹⁰¹(102-digit number)

46385217353680774675…61557656154693883999

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

4.638 × 10¹⁰¹(102-digit number)

46385217353680774675…61557656154693883999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.638 × 10¹⁰¹(102-digit number)

46385217353680774675…61557656154693884001

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

9.277 × 10¹⁰¹(102-digit number)

92770434707361549350…23115312309387767999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.277 × 10¹⁰¹(102-digit number)

92770434707361549350…23115312309387768001

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

1.855 × 10¹⁰²(103-digit number)

18554086941472309870…46230624618775535999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.855 × 10¹⁰²(103-digit number)

18554086941472309870…46230624618775536001

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

3.710 × 10¹⁰²(103-digit number)

37108173882944619740…92461249237551071999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.710 × 10¹⁰²(103-digit number)

37108173882944619740…92461249237551072001

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

7.421 × 10¹⁰²(103-digit number)

74216347765889239480…84922498475102143999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.421 × 10¹⁰²(103-digit number)

74216347765889239480…84922498475102144001

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 #380,542

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