Block #388,457

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/3/2014, 7:47:07 PM · Difficulty 10.4176 · 6,420,558 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6f8202d706e549b13098a79d05be3ebc908938ad342abf9b09276b5194f08064

View on Chainz ↗

Height

#388,457

Difficulty

10.417569

Transactions

Size

1.54 KB

Version

Bits

0a6ae5d1

Nonce

94,010

Timestamp

2/3/2014, 7:47:07 PM

Confirmations

6,420,558

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

410146bfdb7610bada08168dbe81bb03ff81b3bb556fa51f333b1d7b038bef52

Transactions (2)

Coinbasee65a8b881c4535…8004702662a7e7

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

657296beb33e16…df97581138eda5

8 in → 7 out20.0127 XPM1.33 KB

AND9bh7f…Vq85QSAN ARY4njt1…nHyFyfP6 AdKrkQzd…yvN4n1W8 AeKNrjNj…1NEq95Ta AZoyjqWo…cTWTRwva

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.

5.127 × 10¹⁰⁴(105-digit number)

51271065865391293992…69378048029313728449

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

5.127 × 10¹⁰⁴(105-digit number)

51271065865391293992…69378048029313728449

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.127 × 10¹⁰⁴(105-digit number)

51271065865391293992…69378048029313728451

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

1.025 × 10¹⁰⁵(106-digit number)

10254213173078258798…38756096058627456899

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.025 × 10¹⁰⁵(106-digit number)

10254213173078258798…38756096058627456901

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

2.050 × 10¹⁰⁵(106-digit number)

20508426346156517597…77512192117254913799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.050 × 10¹⁰⁵(106-digit number)

20508426346156517597…77512192117254913801

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

4.101 × 10¹⁰⁵(106-digit number)

41016852692313035194…55024384234509827599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.101 × 10¹⁰⁵(106-digit number)

41016852692313035194…55024384234509827601

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

8.203 × 10¹⁰⁵(106-digit number)

82033705384626070388…10048768469019655199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.203 × 10¹⁰⁵(106-digit number)

82033705384626070388…10048768469019655201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.640 × 10¹⁰⁶(107-digit number)

16406741076925214077…20097536938039310399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #388,457

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