Block #641,108

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/20/2014, 5:58:28 PM · Difficulty 10.9575 · 6,185,507 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4d7d1c379bbe5b9445cb800d94711136d75607b6b232abf6f4153eab365fd266

View on Chainz ↗

Height

#641,108

Difficulty

10.957504

Transactions

Size

1.37 KB

Version

Bits

0af51ef9

Nonce

897,655,211

Timestamp

7/20/2014, 5:58:28 PM

Confirmations

6,185,507

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

d1c7d68b7d3cef5195f2d76ccb185c27179dba6ca088fe9a71ee9514f8e533e2

Transactions (5)

Coinbase61045b03fcadde…4b825829ed36ac

1 in → 1 out8.3600 XPM116 B

ANSXnLY2…Sd25TjkD

56ccccb2837d16…efe59f2ea73dd9

3 in → 2 out24.9200 XPM519 B

AU7J9y8g…3cPN7iGT AKQb78kd…kP7kYNJq

63ab0a39846cfe…190e2293d5190a

1 in → 2 out8.3000 XPM226 B

AaLJgmbn…Czvk1jBR AcKerPva…qeeuPChG

6c9f82b1dd5a61…09d1294b3a98d3

1 in → 2 out8.3000 XPM227 B

AYU1Ynxb…6LNs2ZYM AeV9JwmU…YEEQGnpc

974a254fb10eed…f66a4af4305688

1 in → 2 out8.3000 XPM226 B

ATUJFkEF…j71DTZhm Ac6gnQyP…pRvFTkxS

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.

5.133 × 10⁹⁸(99-digit number)

51334389361608042148…63113389419425955839

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

5.133 × 10⁹⁸(99-digit number)

51334389361608042148…63113389419425955839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.133 × 10⁹⁸(99-digit number)

51334389361608042148…63113389419425955841

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

1.026 × 10⁹⁹(100-digit number)

10266877872321608429…26226778838851911679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.026 × 10⁹⁹(100-digit number)

10266877872321608429…26226778838851911681

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

2.053 × 10⁹⁹(100-digit number)

20533755744643216859…52453557677703823359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.053 × 10⁹⁹(100-digit number)

20533755744643216859…52453557677703823361

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

4.106 × 10⁹⁹(100-digit number)

41067511489286433718…04907115355407646719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.106 × 10⁹⁹(100-digit number)

41067511489286433718…04907115355407646721

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

8.213 × 10⁹⁹(100-digit number)

82135022978572867437…09814230710815293439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.213 × 10⁹⁹(100-digit number)

82135022978572867437…09814230710815293441

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

1.642 × 10¹⁰⁰(101-digit number)

16427004595714573487…19628461421630586879

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 #641,108

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