Block #353,392

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/10/2014, 10:06:44 PM · Difficulty 10.3253 · 6,455,507 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

83f5e52864ef48f3c50a624b72760ba79d5a96baf72f7b973a3bef4bb6aa01c3

View on Chainz ↗

Height

#353,392

Difficulty

10.325297

Transactions

Size

881 B

Version

Bits

0a5346a4

Nonce

10,582

Timestamp

1/10/2014, 10:06:44 PM

Confirmations

6,455,507

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

d840e59af40b06cd3c7c97f15c3ee9b2e05b4a037d919da5c61214dddcf82f22

Transactions (4)

Coinbasefd0a6d0865122a…b0e476f5da5656

1 in → 1 out9.4000 XPM110 B

AeKNrjNj…1NEq95Ta

322b776baa3a2d…dd4b117ac947d2

1 in → 2 out8.4031 XPM226 B

AeApQQZY…wdQ7FcUn Adg4Rjpt…46vsgysh

aea3f352c55286…cb40c0b754739c

1 in → 2 out8.4068 XPM226 B

AZDVbg2y…VLZehZLR AGwbWtsv…KdCfVEHS

c4249cfeb20510…d9efc75cf57bf9

1 in → 2 out8.4081 XPM226 B

AeensNaB…nXDdKXir AM1Vgavn…YqZvyMg1

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.

1.222 × 10¹⁰²(103-digit number)

12226864280735131303…90948322572444483839

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

1.222 × 10¹⁰²(103-digit number)

12226864280735131303…90948322572444483839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.222 × 10¹⁰²(103-digit number)

12226864280735131303…90948322572444483841

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

2.445 × 10¹⁰²(103-digit number)

24453728561470262606…81896645144888967679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.445 × 10¹⁰²(103-digit number)

24453728561470262606…81896645144888967681

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

4.890 × 10¹⁰²(103-digit number)

48907457122940525212…63793290289777935359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.890 × 10¹⁰²(103-digit number)

48907457122940525212…63793290289777935361

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

9.781 × 10¹⁰²(103-digit number)

97814914245881050424…27586580579555870719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.781 × 10¹⁰²(103-digit number)

97814914245881050424…27586580579555870721

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

1.956 × 10¹⁰³(104-digit number)

19562982849176210084…55173161159111741439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.956 × 10¹⁰³(104-digit number)

19562982849176210084…55173161159111741441

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 #353,392

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