Block #138,984

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/28/2013, 5:41:21 PM · Difficulty 9.8292 · 6,669,399 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

38c70f7bb6a7cfafdf871cdb08958e1a74693fc9644debdfc468322f2e7d39b7

View on Chainz ↗

Height

#138,984

Difficulty

9.829226

Transactions

Size

1006 B

Version

Bits

09d44821

Nonce

93,145

Timestamp

8/28/2013, 5:41:21 PM

Confirmations

6,669,399

Mined by

⛏️ P2SHAbGkvdxHZ4BVXfnK4PvSdcrNAUoihMdBXd

Merkle Root

4749f2c482e76f4b54200dd688a61a8fc6c6eb6cf976e03c815d84e864ed207f

Transactions (2)

Coinbase5b672b65b4c33f…f9337d33df6be8

1 in → 1 out10.3500 XPM100 B

AbGkvdxH…oihMdBXd

3251af8579d677…76345eb0668dd6

5 in → 2 out1499.9656 XPM817 B

AVq7Gfae…HzDW6cAo AXM24e2K…DRGJC2vA

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.

1.307 × 10⁹¹(92-digit number)

13075452861997748267…53227784350454320729

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

1.307 × 10⁹¹(92-digit number)

13075452861997748267…53227784350454320729

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.307 × 10⁹¹(92-digit number)

13075452861997748267…53227784350454320731

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

2.615 × 10⁹¹(92-digit number)

26150905723995496535…06455568700908641459

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.615 × 10⁹¹(92-digit number)

26150905723995496535…06455568700908641461

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

5.230 × 10⁹¹(92-digit number)

52301811447990993071…12911137401817282919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.230 × 10⁹¹(92-digit number)

52301811447990993071…12911137401817282921

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

1.046 × 10⁹²(93-digit number)

10460362289598198614…25822274803634565839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.046 × 10⁹²(93-digit number)

10460362289598198614…25822274803634565841

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

2.092 × 10⁹²(93-digit number)

20920724579196397228…51644549607269131679

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 #138,984

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