Block #2,640,506

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/1/2018, 12:50:55 AM · Difficulty 11.5836 · 4,201,488 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b2c0816bdcfed1ecc828afd492da8eef06e6b6bf8613908917fb29a0e8546018

View on Chainz ↗

Height

#2,640,506

Difficulty

11.583627

Transactions

Size

575 B

Version

Bits

0b95688d

Nonce

376,811,241

Timestamp

5/1/2018, 12:50:55 AM

Confirmations

4,201,488

Mined by

⛏️ P2SHALRBjUjPHBExBj8Kn5oW3LfogJTgAbS3ZM

Merkle Root

3112ae159e91082d362ed4dda932536a3c931040928bb4b996b0136d56c9daa3

Transactions (2)

Coinbase16b6b66c37c284…1c95cd89cb799c

1 in → 1 out7.4500 XPM110 B

ALRBjUjP…TgAbS3ZM

2984249216c9f5…b68fb7d868c585

2 in → 2 out10.5400 XPM374 B

AXYgXMrN…yqx8mHPc ATToo7Cy…EUMwyyiv

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.

1.005 × 10⁹⁷(98-digit number)

10053883431320244280…29068619283335352319

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

1.005 × 10⁹⁷(98-digit number)

10053883431320244280…29068619283335352319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.005 × 10⁹⁷(98-digit number)

10053883431320244280…29068619283335352321

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

2.010 × 10⁹⁷(98-digit number)

20107766862640488560…58137238566670704639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.010 × 10⁹⁷(98-digit number)

20107766862640488560…58137238566670704641

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

4.021 × 10⁹⁷(98-digit number)

40215533725280977121…16274477133341409279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.021 × 10⁹⁷(98-digit number)

40215533725280977121…16274477133341409281

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

8.043 × 10⁹⁷(98-digit number)

80431067450561954243…32548954266682818559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.043 × 10⁹⁷(98-digit number)

80431067450561954243…32548954266682818561

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

1.608 × 10⁹⁸(99-digit number)

16086213490112390848…65097908533365637119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.608 × 10⁹⁸(99-digit number)

16086213490112390848…65097908533365637121

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

3.217 × 10⁹⁸(99-digit number)

32172426980224781697…30195817066731274239

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 #2,640,506

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