Block #511,774

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/26/2014, 11:21:46 AM · Difficulty 10.8307 · 6,312,715 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f9fff8c68a4005c0dcfdb096af326a698473ee978a8a72ef2b718b4706f44e05

View on Chainz ↗

Height

#511,774

Difficulty

10.830732

Transactions

Size

4.84 KB

Version

Bits

0ad4aae2

Nonce

584,906,807

Timestamp

4/26/2014, 11:21:46 AM

Confirmations

6,312,715

Mined by

⛏️ P2SHAHBUbUMH8ZLmrgXzYfyfU4jeVoy4xve4TQ

Merkle Root

260126d6f70ae15980f0115b3ddbabe688c3227fc84bc6f7e296b3c4fcfcdc9f

Transactions (5)

Coinbaseea6b2299de4e80…a672b636d50b81

1 in → 1 out8.5900 XPM109 B

AHBUbUMH…y4xve4TQ

199bb397c79a47…94ef7a7039d96f

27 in → 2 out25.7112 XPM3.98 KB

AXnXEwg6…un9Teu49 AGfn4Mdp…U2vzwqrD

0370d5a6d83266…67fe294384dbc0

1 in → 2 out5.9537 XPM226 B

AQA68CNC…njuffCDB AWr7QESV…T91HodnJ

1af8dd5a1d767f…aa9b36bc961ff9

1 in → 2 out5.7819 XPM226 B

AdCzYx3G…T4cwGbGS AM23VEk3…q622MtoH

9d2339060d55f0…040e5878cdd80d

1 in → 2 out0.7841 XPM226 B

AYjwdqha…PWTkrAsC AGdWVjRk…LFVsqCnK

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.

2.706 × 10⁸⁹(90-digit number)

27069210996850789091…79726656749773782349

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

2.706 × 10⁸⁹(90-digit number)

27069210996850789091…79726656749773782349

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.706 × 10⁸⁹(90-digit number)

27069210996850789091…79726656749773782351

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

5.413 × 10⁸⁹(90-digit number)

54138421993701578183…59453313499547564699

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.413 × 10⁸⁹(90-digit number)

54138421993701578183…59453313499547564701

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

1.082 × 10⁹⁰(91-digit number)

10827684398740315636…18906626999095129399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.082 × 10⁹⁰(91-digit number)

10827684398740315636…18906626999095129401

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

2.165 × 10⁹⁰(91-digit number)

21655368797480631273…37813253998190258799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.165 × 10⁹⁰(91-digit number)

21655368797480631273…37813253998190258801

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

4.331 × 10⁹⁰(91-digit number)

43310737594961262546…75626507996380517599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.331 × 10⁹⁰(91-digit number)

43310737594961262546…75626507996380517601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #511,774

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