Block #351,685

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/9/2014, 8:41:35 PM · Difficulty 10.3000 · 6,458,203 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3b2a020b23cfd5a459bdce9757b01f1c84f18d49a75def056790f59d258af0f7

View on Chainz ↗

Height

#351,685

Difficulty

10.300044

Transactions

Size

1.36 KB

Version

Bits

0a4ccfb7

Nonce

20,146

Timestamp

1/9/2014, 8:41:35 PM

Confirmations

6,458,203

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

eb04f0e9841ba6e8daecc558c7e95df8143dd8cde380239ad187c71bc0314f05

Transactions (3)

Coinbased77f8502b6c4ed…9395517a7879c8

1 in → 1 out9.4300 XPM110 B

AeKNrjNj…1NEq95Ta

09804e0248090a…c3b19993db79a9

1 in → 2 out9.4800 XPM226 B

ARtRK82P…dR1TETE6 AR7BsVgY…cBPcAhhF

efe62d2f1ed874…40c3a8ae56e65a

6 in → 2 out19.4284 XPM965 B

AJKgvokB…69CkANMW AJHQpqCb…DnKqZb4H

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.

2.276 × 10¹⁰⁰(101-digit number)

22766193322676904268…16606579298126218239

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

2.276 × 10¹⁰⁰(101-digit number)

22766193322676904268…16606579298126218239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.276 × 10¹⁰⁰(101-digit number)

22766193322676904268…16606579298126218241

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

4.553 × 10¹⁰⁰(101-digit number)

45532386645353808537…33213158596252436479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.553 × 10¹⁰⁰(101-digit number)

45532386645353808537…33213158596252436481

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

9.106 × 10¹⁰⁰(101-digit number)

91064773290707617075…66426317192504872959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.106 × 10¹⁰⁰(101-digit number)

91064773290707617075…66426317192504872961

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

1.821 × 10¹⁰¹(102-digit number)

18212954658141523415…32852634385009745919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.821 × 10¹⁰¹(102-digit number)

18212954658141523415…32852634385009745921

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

3.642 × 10¹⁰¹(102-digit number)

36425909316283046830…65705268770019491839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.642 × 10¹⁰¹(102-digit number)

36425909316283046830…65705268770019491841

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 #351,685

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