Block #510,875

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/25/2014, 9:59:29 PM · Difficulty 10.8274 · 6,298,832 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3a1ec8cc7f075d8d230307a5d9da9512c266ecb8216e27bb7b37c24c1120b547

View on Chainz ↗

Height

#510,875

Difficulty

10.827424

Transactions

Size

1.37 KB

Version

Bits

0ad3d212

Nonce

54,448,054

Timestamp

4/25/2014, 9:59:29 PM

Confirmations

6,298,832

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

6684c2000d944c018c690998f0367b665fa3b62c35f0519fd9e3616fb9a996ed

Transactions (3)

Coinbased97a868bf5f481…e3dd45ec5dba52

1 in → 1 out8.5400 XPM116 B

AbwWkWZt…kawDhufa

0a02d5201a9c21…4c511f9b01b372

1 in → 2 out3.0024 XPM227 B

AbpBeGmy…EGdqBSj5 AG8u7ddV…cU5QJSqk

7160fcd0466d82…b34c0340cc1f36

6 in → 2 out5.0839 XPM965 B

AXLffwxx…zkHEyYdn AGr6YkiV…71aRe1d5

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.

1.055 × 10¹⁰¹(102-digit number)

10557365595452734417…61626670285331374079

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

1.055 × 10¹⁰¹(102-digit number)

10557365595452734417…61626670285331374079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.055 × 10¹⁰¹(102-digit number)

10557365595452734417…61626670285331374081

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

2.111 × 10¹⁰¹(102-digit number)

21114731190905468835…23253340570662748159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.111 × 10¹⁰¹(102-digit number)

21114731190905468835…23253340570662748161

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

4.222 × 10¹⁰¹(102-digit number)

42229462381810937671…46506681141325496319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.222 × 10¹⁰¹(102-digit number)

42229462381810937671…46506681141325496321

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

8.445 × 10¹⁰¹(102-digit number)

84458924763621875343…93013362282650992639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.445 × 10¹⁰¹(102-digit number)

84458924763621875343…93013362282650992641

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

1.689 × 10¹⁰²(103-digit number)

16891784952724375068…86026724565301985279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.689 × 10¹⁰²(103-digit number)

16891784952724375068…86026724565301985281

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 #510,875

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