Block #2,660,416

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/14/2018, 9:43:59 AM · Difficulty 11.6355 · 4,171,939 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bd8bae6cf70c9b4160f0811154b073174b2a16196a711b8f88e92c35df234b21

View on Chainz ↗

Height

#2,660,416

Difficulty

11.635460

Transactions

Size

799 B

Version

Bits

0ba2ad7c

Nonce

29,103,578

Timestamp

5/14/2018, 9:43:59 AM

Confirmations

4,171,939

Mined by

⛏️ P2SHAV3buqUwaVZqLeUmYdwUSKYhd2tvsrk9LW

Merkle Root

034ff76310a8aa8ca1e1dbae252c3451e1b3215ce3f37936a96b626b0fce9332

Transactions (3)

Coinbase525956f931a64d…d91f927d745893

1 in → 1 out7.3900 XPM110 B

AV3buqUw…tvsrk9LW

61d6a2b6526fa7…81b4dd948b2f97

2 in → 2 out6.5368 XPM375 B

Ab61RUd9…Ej2QSUZW AdxXry6p…3LAt843S

7a4d043ce9fd49…cb4273d6ed4084

1 in → 2 out1.2579 XPM225 B

ARfZ9g5N…JNQym6nH ALvrNVZd…WWVpyiCu

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.

1.700 × 10⁹²(93-digit number)

17004233417492136928…89093561322765126539

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

1.700 × 10⁹²(93-digit number)

17004233417492136928…89093561322765126539

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.700 × 10⁹²(93-digit number)

17004233417492136928…89093561322765126541

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

3.400 × 10⁹²(93-digit number)

34008466834984273856…78187122645530253079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.400 × 10⁹²(93-digit number)

34008466834984273856…78187122645530253081

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

6.801 × 10⁹²(93-digit number)

68016933669968547712…56374245291060506159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.801 × 10⁹²(93-digit number)

68016933669968547712…56374245291060506161

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

1.360 × 10⁹³(94-digit number)

13603386733993709542…12748490582121012319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.360 × 10⁹³(94-digit number)

13603386733993709542…12748490582121012321

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

2.720 × 10⁹³(94-digit number)

27206773467987419084…25496981164242024639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.720 × 10⁹³(94-digit number)

27206773467987419084…25496981164242024641

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

5.441 × 10⁹³(94-digit number)

54413546935974838169…50993962328484049279

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 #2,660,416

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