Block #511,775

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/26/2014, 11:22:13 AM · Difficulty 10.8307 · 6,315,276 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

25fd303554e0e6ebfa3002c7beadc8be6533c6f875a42cc4f5b1786b2c6722d9

View on Chainz ↗

Height

#511,775

Difficulty

10.830736

Transactions

Size

208 B

Version

Bits

0ad4ab24

Nonce

20,069,460

Timestamp

4/26/2014, 11:22:13 AM

Confirmations

6,315,276

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

1d9fa84500270239b568307762052fbd637e135dcfb56bae74b673ce2a0fbb1a

Transactions (1)

Coinbase1d9fa845002702…b673ce2a0fbb1a

1 in → 1 out8.5100 XPM116 B

AbwWkWZt…kawDhufa

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.

1.065 × 10¹⁰⁰(101-digit number)

10655491349453900139…04945933331152540159

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

1.065 × 10¹⁰⁰(101-digit number)

10655491349453900139…04945933331152540159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.065 × 10¹⁰⁰(101-digit number)

10655491349453900139…04945933331152540161

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

2.131 × 10¹⁰⁰(101-digit number)

21310982698907800278…09891866662305080319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.131 × 10¹⁰⁰(101-digit number)

21310982698907800278…09891866662305080321

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

4.262 × 10¹⁰⁰(101-digit number)

42621965397815600557…19783733324610160639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.262 × 10¹⁰⁰(101-digit number)

42621965397815600557…19783733324610160641

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

8.524 × 10¹⁰⁰(101-digit number)

85243930795631201114…39567466649220321279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.524 × 10¹⁰⁰(101-digit number)

85243930795631201114…39567466649220321281

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

1.704 × 10¹⁰¹(102-digit number)

17048786159126240222…79134933298440642559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.704 × 10¹⁰¹(102-digit number)

17048786159126240222…79134933298440642561

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

3.409 × 10¹⁰¹(102-digit number)

34097572318252480445…58269866596881285119

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 #511,775

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