Block #783,481

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/26/2014, 5:31:07 AM · Difficulty 10.9751 · 6,031,662 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

db5605f4a3e26405c4128cfa8a8ac23a8f2de5f8bf965cf767bbd88bb9af12e8

View on Chainz ↗

Height

#783,481

Difficulty

10.975093

Transactions

Size

1.66 KB

Version

Bits

0af99faa

Nonce

177,377,802

Timestamp

10/26/2014, 5:31:07 AM

Confirmations

6,031,662

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

2b39e62c091970c3f73e7d28008486ee395dfb97ce919055ffb9298e573a9d50

Transactions (5)

Coinbasef72f5cc72bbbf0…ec16e17f685632

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

ea8ff4506b52b4…f9c044953ef86b

1 in → 2 out8.2700 XPM226 B

AMoJsji6…a13Bp22Q AcNpQkZZ…rsojRhgL

34c16db0d71a8d…7774dc29a25c75

1 in → 2 out7.3163 XPM226 B

ARQdcbYT…Qj6b2EyA AGdWVjRk…LFVsqCnK

dae2575b3b92f0…27469b99ceec63

1 in → 2 out7.2475 XPM226 B

AL6SxEF5…fohpGbvu AcKerPva…qeeuPChG

749fd5025f21c6…67a15917764357

5 in → 2 out0.5218 XPM815 B

AXt4NoiW…5DuknjnE AWeFTqSF…usRDA3NM

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.

2.570 × 10⁹⁹(100-digit number)

25703813887972891399…76120175398108364799

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

2.570 × 10⁹⁹(100-digit number)

25703813887972891399…76120175398108364799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.570 × 10⁹⁹(100-digit number)

25703813887972891399…76120175398108364801

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

5.140 × 10⁹⁹(100-digit number)

51407627775945782798…52240350796216729599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.140 × 10⁹⁹(100-digit number)

51407627775945782798…52240350796216729601

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

1.028 × 10¹⁰⁰(101-digit number)

10281525555189156559…04480701592433459199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.028 × 10¹⁰⁰(101-digit number)

10281525555189156559…04480701592433459201

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

2.056 × 10¹⁰⁰(101-digit number)

20563051110378313119…08961403184866918399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.056 × 10¹⁰⁰(101-digit number)

20563051110378313119…08961403184866918401

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

4.112 × 10¹⁰⁰(101-digit number)

41126102220756626238…17922806369733836799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.112 × 10¹⁰⁰(101-digit number)

41126102220756626238…17922806369733836801

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

8.225 × 10¹⁰⁰(101-digit number)

82252204441513252476…35845612739467673599

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 #783,481

Cookie Preferences