Block #776,158

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/20/2014, 1:33:40 AM · Difficulty 10.9815 · 6,031,071 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4f344fe44558e049d62a8fc9041bf7479acece103d938b485051e8f3a68e5481

View on Chainz ↗

Height

#776,158

Difficulty

10.981520

Transactions

Size

661 B

Version

Bits

0afb44ed

Nonce

2,747,419,383

Timestamp

10/20/2014, 1:33:40 AM

Confirmations

6,031,071

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

6301f77bba96db5d8b756e7debba2adbb75ddb62346b826f81f3eb2be061f09e

Transactions (3)

Coinbasefea1c660b8e213…1d55cb024c15ca

1 in → 1 out8.3000 XPM116 B

ANSXnLY2…Sd25TjkD

dbac1f0ae3a5ae…c2815b558c388b

1 in → 2 out6.1972 XPM227 B

AcKerPva…qeeuPChG Aa8N7MWS…2YgZCwwz

6bc75620993fdd…7391c8eee6c9ed

1 in → 2 out6.1124 XPM226 B

ANyTjLwF…5UCoSZLQ AMA1JjCx…bG9Y2mPM

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.

6.434 × 10⁹⁹(100-digit number)

64345331813514714624…09229603676271411199

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

6.434 × 10⁹⁹(100-digit number)

64345331813514714624…09229603676271411199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.434 × 10⁹⁹(100-digit number)

64345331813514714624…09229603676271411201

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

1.286 × 10¹⁰⁰(101-digit number)

12869066362702942924…18459207352542822399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.286 × 10¹⁰⁰(101-digit number)

12869066362702942924…18459207352542822401

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

2.573 × 10¹⁰⁰(101-digit number)

25738132725405885849…36918414705085644799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.573 × 10¹⁰⁰(101-digit number)

25738132725405885849…36918414705085644801

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

5.147 × 10¹⁰⁰(101-digit number)

51476265450811771699…73836829410171289599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.147 × 10¹⁰⁰(101-digit number)

51476265450811771699…73836829410171289601

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

1.029 × 10¹⁰¹(102-digit number)

10295253090162354339…47673658820342579199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.029 × 10¹⁰¹(102-digit number)

10295253090162354339…47673658820342579201

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

2.059 × 10¹⁰¹(102-digit number)

20590506180324708679…95347317640685158399

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 #776,158

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