Block #2,649,445

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/5/2018, 6:17:50 AM · Difficulty 11.7638 · 4,191,663 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b0314fdfeafb2cbf722423c4b25a54b79f5d18e5e5c25ff4b2f1e821734e07b9

View on Chainz ↗

Height

#2,649,445

Difficulty

11.763826

Transactions

Size

1.19 KB

Version

Bits

0bc38a17

Nonce

317,548,037

Timestamp

5/5/2018, 6:17:50 AM

Confirmations

4,191,663

Mined by

⛏️ P2SHAH9PAHyXZssc7GH9iZSbeekiQ9x5yxyYCE

Merkle Root

f0b977598be2f18074eeae0ad7be210632c67e7f96a776e4114d9c7e38234871

Transactions (5)

Coinbase20138b92c79a70…94adb6e3e454d3

1 in → 1 out7.2500 XPM110 B

AH9PAHyX…x5yxyYCE

ba52c1edaf4bd6…e5257f639904d6

1 in → 2 out7.2200 XPM193 B

AbkujpLP…dXHngHYW ALh5G3Np…6TsNC2wj

dc3985250396bc…412b0bc14c4375

2 in → 2 out2.2038 XPM374 B

APw7prZm…NQx9Tk2i AYMYyv12…vRhMgUZp

5ade537bb52101…393677b5b5a3f8

1 in → 2 out4.5663 XPM226 B

AHSDnxWz…yP5fr5Ne AMwmR7Md…T1b83Bab

19e405ab484d2f…5d81723ca64bf3

1 in → 2 out1.8409 XPM226 B

AKJa6cp2…asUBxgcZ AP8Rtrtc…SfENdmKQ

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.

5.069 × 10⁹⁵(96-digit number)

50699485450224857899…71002315456290315439

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

5.069 × 10⁹⁵(96-digit number)

50699485450224857899…71002315456290315439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.069 × 10⁹⁵(96-digit number)

50699485450224857899…71002315456290315441

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

1.013 × 10⁹⁶(97-digit number)

10139897090044971579…42004630912580630879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.013 × 10⁹⁶(97-digit number)

10139897090044971579…42004630912580630881

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

2.027 × 10⁹⁶(97-digit number)

20279794180089943159…84009261825161261759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.027 × 10⁹⁶(97-digit number)

20279794180089943159…84009261825161261761

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

4.055 × 10⁹⁶(97-digit number)

40559588360179886319…68018523650322523519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.055 × 10⁹⁶(97-digit number)

40559588360179886319…68018523650322523521

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

8.111 × 10⁹⁶(97-digit number)

81119176720359772639…36037047300645047039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.111 × 10⁹⁶(97-digit number)

81119176720359772639…36037047300645047041

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

1.622 × 10⁹⁷(98-digit number)

16223835344071954527…72074094601290094079

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 #2,649,445

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