Block #510,911

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/25/2014, 10:19:26 PM · Difficulty 10.8280 · 6,296,943 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b41a657589201b1eac778c5612867fe4087dccf85d400d5f0749f4270de69d0b

View on Chainz ↗

Height

#510,911

Difficulty

10.828006

Transactions

Size

1.47 KB

Version

Bits

0ad3f832

Nonce

350,159

Timestamp

4/25/2014, 10:19:26 PM

Confirmations

6,296,943

Mined by

⛏️ aSZiATKK7iFzxU98qfet38JZnUDJ7swZm46KN1

Merkle Root

63bd3c6a7f741b8a605a140ed71e175bd99e840b090b8e4c6d7a0d64b21216ae

Transactions (4)

Coinbase83fd3a42571716…c747f2c4bf112c

1 in → 20 out8.5200 XPM742 B

ATKK7iFz…wZm46KN1 AQvZBsUo…hppgRZTJ ALqxX1WA…hsKjbnXn AJzWx2VD…j4ZSMit5 ANNg88pG…ppn21sTe

abbe9e96bd401c…f9c70cc13340ee

1 in → 2 out6.9864 XPM227 B

ARYuxktH…PAJctg1M ANcJBG4q…jhjpab9q

79e180b1598d5f…4f5493b0c7402d

1 in → 2 out6.8599 XPM225 B

AKUKhLig…GRhbxePP AM8GuxnN…AfjbhWoV

dcc811ef94e801…f8145a17810644

1 in → 2 out4.9652 XPM226 B

ARKdhbSb…2K2B78FE AXPjDsq5…ep9XQVRb

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.

1.342 × 10⁹⁴(95-digit number)

13428810459396472064…87604556991339321059

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

1.342 × 10⁹⁴(95-digit number)

13428810459396472064…87604556991339321059

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.342 × 10⁹⁴(95-digit number)

13428810459396472064…87604556991339321061

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

2.685 × 10⁹⁴(95-digit number)

26857620918792944128…75209113982678642119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.685 × 10⁹⁴(95-digit number)

26857620918792944128…75209113982678642121

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

5.371 × 10⁹⁴(95-digit number)

53715241837585888257…50418227965357284239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.371 × 10⁹⁴(95-digit number)

53715241837585888257…50418227965357284241

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

1.074 × 10⁹⁵(96-digit number)

10743048367517177651…00836455930714568479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.074 × 10⁹⁵(96-digit number)

10743048367517177651…00836455930714568481

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

2.148 × 10⁹⁵(96-digit number)

21486096735034355303…01672911861429136959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.148 × 10⁹⁵(96-digit number)

21486096735034355303…01672911861429136961

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 #510,911

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