Block #117,975

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/15/2013, 10:52:46 AM · Difficulty 9.7509 · 6,678,499 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3d73166de2731b1af952b3e96354e9be4ce003802d3345b626a77fe1f36f720c

View on Chainz ↗

Height

#117,975

Difficulty

9.750897

Transactions

Size

721 B

Version

Bits

09c03acd

Nonce

180,163

Timestamp

8/15/2013, 10:52:46 AM

Confirmations

6,678,499

Mined by

⛏️ P2SHAQiPiEbTq6okvE2YdA46DgYRZ8c8WPtuxp

Merkle Root

e5c3ddcef43f2d1b33f5ca3f997a3875415e43b9236998b834239371af7cfcff

Transactions (2)

Coinbase9e78b27fa499d7…3861cad527123c

1 in → 1 out10.5100 XPM109 B

AQiPiEbT…c8WPtuxp

bf0de170d461a9…d5aa6206b86fb0

3 in → 2 out385.4456 XPM521 B

AcvCX7XD…5uYpxvK4 AS7B6ZGo…WJvjDEXG

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.

2.034 × 10⁹⁸(99-digit number)

20348142849410378048…99393634494364031839

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

2.034 × 10⁹⁸(99-digit number)

20348142849410378048…99393634494364031839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.034 × 10⁹⁸(99-digit number)

20348142849410378048…99393634494364031841

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

4.069 × 10⁹⁸(99-digit number)

40696285698820756097…98787268988728063679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.069 × 10⁹⁸(99-digit number)

40696285698820756097…98787268988728063681

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

8.139 × 10⁹⁸(99-digit number)

81392571397641512195…97574537977456127359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.139 × 10⁹⁸(99-digit number)

81392571397641512195…97574537977456127361

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

1.627 × 10⁹⁹(100-digit number)

16278514279528302439…95149075954912254719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.627 × 10⁹⁹(100-digit number)

16278514279528302439…95149075954912254721

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

3.255 × 10⁹⁹(100-digit number)

32557028559056604878…90298151909824509439

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