Block #123,442

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/19/2013, 1:39:16 AM · Difficulty 9.7639 · 6,680,266 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fb13918d62ae1a0422fdc4193256c1a07e38d689e99219cb1a670cd99ef024aa

View on Chainz ↗

Height

#123,442

Difficulty

9.763889

Transactions

Size

8.22 KB

Version

Bits

09c38e3d

Nonce

254,838

Timestamp

8/19/2013, 1:39:16 AM

Confirmations

6,680,266

Mined by

⛏️ P2SHAVTdASf7qnnupKKcKsNC2y3u9VwQZLqRtu

Merkle Root

8f5a673b8b6fac0d792bf1370bab0865b76745588ebfad3d50b11dc3cfc0820c

Transactions (2)

Coinbaseb1b6fbdddec769…9471f7815a5f57

1 in → 1 out10.5600 XPM109 B

AVTdASf7…wQZLqRtu

b3a836c7a111e8…ed72e9330062f7

55 in → 2 out110.6396 XPM8.03 KB

ATaAsdHP…zkdKRHXB AWfJ3yAB…bmiTKueS

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.

3.281 × 10⁹⁴(95-digit number)

32812184686973027889…40414207923926978139

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

3.281 × 10⁹⁴(95-digit number)

32812184686973027889…40414207923926978139

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.281 × 10⁹⁴(95-digit number)

32812184686973027889…40414207923926978141

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

6.562 × 10⁹⁴(95-digit number)

65624369373946055779…80828415847853956279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.562 × 10⁹⁴(95-digit number)

65624369373946055779…80828415847853956281

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

1.312 × 10⁹⁵(96-digit number)

13124873874789211155…61656831695707912559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.312 × 10⁹⁵(96-digit number)

13124873874789211155…61656831695707912561

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

2.624 × 10⁹⁵(96-digit number)

26249747749578422311…23313663391415825119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.624 × 10⁹⁵(96-digit number)

26249747749578422311…23313663391415825121

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

5.249 × 10⁹⁵(96-digit number)

52499495499156844623…46627326782831650239

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