Block #408,414

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/17/2014, 3:38:55 PM · Difficulty 10.4308 · 6,402,529 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bccf975f71052be372d76c7f27382af6f335b6baf04600d0b4eb9e04e6938b1f

View on Chainz ↗

Height

#408,414

Difficulty

10.430781

Transactions

Size

1.94 KB

Version

Bits

0a6e47a5

Nonce

293,206

Timestamp

2/17/2014, 3:38:55 PM

Confirmations

6,402,529

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

f7be5acfee000c175dc7094c013dc603f42fdb2971fc8f394698c39116ee7780

Transactions (5)

Coinbase295f37b718b2fc…f664740544d6d3

1 in → 1 out9.2300 XPM110 B

AeKNrjNj…1NEq95Ta

9ffb41b08febbb…b35f58436a7b31

2 in → 1 out139.3336 XPM340 B

ANhigdUH…hrv5inM2

b80db37f947fe1…93d454c3dbf8fe

2 in → 2 out12.2564 XPM374 B

AHXYvSCP…9tN89hht APaSkzEP…e9f176Qr

da2f4354c5d790…c89b9d93bd0c0f

4 in → 10 out28.1792 XPM840 B

ANVQgy2y…heyFibjn ALDdaWxb…47UZU4H8 AMeyeZ9L…gJoDemgf AGaij5dN…mmh48Z5W AXDEZh15…FbrAPGkC

243ff2059e07eb…9c5b70976093bc

1 in → 2 out3.9844 XPM227 B

AVWPtEJA…bGAToibP APVMZmfa…GvUTmvdb

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.

3.011 × 10¹⁰⁰(101-digit number)

30114171141877963527…24504277991429505279

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

3.011 × 10¹⁰⁰(101-digit number)

30114171141877963527…24504277991429505279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.011 × 10¹⁰⁰(101-digit number)

30114171141877963527…24504277991429505281

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

6.022 × 10¹⁰⁰(101-digit number)

60228342283755927055…49008555982859010559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.022 × 10¹⁰⁰(101-digit number)

60228342283755927055…49008555982859010561

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

1.204 × 10¹⁰¹(102-digit number)

12045668456751185411…98017111965718021119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.204 × 10¹⁰¹(102-digit number)

12045668456751185411…98017111965718021121

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

2.409 × 10¹⁰¹(102-digit number)

24091336913502370822…96034223931436042239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.409 × 10¹⁰¹(102-digit number)

24091336913502370822…96034223931436042241

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

4.818 × 10¹⁰¹(102-digit number)

48182673827004741644…92068447862872084479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.818 × 10¹⁰¹(102-digit number)

48182673827004741644…92068447862872084481

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 #408,414

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