Block #102,340

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/7/2013, 2:14:06 AM · Difficulty 9.4904 · 6,724,636 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

778c03dd38cf6a2be570dbf28b0658e69ab6943cd7d9de22d26936a2779e0352

View on Chainz ↗

Height

#102,340

Difficulty

9.490376

Transactions

Size

619 B

Version

Bits

097d8949

Nonce

515,313

Timestamp

8/7/2013, 2:14:06 AM

Confirmations

6,724,636

Mined by

⛏️ P2SHAGNF5FM1iDMi8svUwibLBo1iJFn54CJy51

Merkle Root

af02f1a8d5febf81d432e348cc5565ac957857b79f6a555e1011792b6e1ba3b3

Transactions (3)

Coinbasecdb2f257f3eaaf…dd6135384a1fc7

1 in → 1 out11.1100 XPM109 B

AGNF5FM1…n54CJy51

3031317f67182c…68c093e6f3798b

1 in → 2 out1.9911 XPM227 B

AGsjwwbj…Fq54UcrM Ab8H9PTp…woHhCiZZ

ed4f12a4e8293e…5f6c149c621d85

1 in → 1 out1.9950 XPM192 B

AVB82gtg…uPRBzcfn

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.

6.630 × 10⁹⁷(98-digit number)

66308045447818195610…75773738839769023559

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

6.630 × 10⁹⁷(98-digit number)

66308045447818195610…75773738839769023559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.630 × 10⁹⁷(98-digit number)

66308045447818195610…75773738839769023561

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

1.326 × 10⁹⁸(99-digit number)

13261609089563639122…51547477679538047119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.326 × 10⁹⁸(99-digit number)

13261609089563639122…51547477679538047121

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

2.652 × 10⁹⁸(99-digit number)

26523218179127278244…03094955359076094239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.652 × 10⁹⁸(99-digit number)

26523218179127278244…03094955359076094241

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

5.304 × 10⁹⁸(99-digit number)

53046436358254556488…06189910718152188479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.304 × 10⁹⁸(99-digit number)

53046436358254556488…06189910718152188481

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

1.060 × 10⁹⁹(100-digit number)

10609287271650911297…12379821436304376959

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #102,340

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