Block #502,052

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/20/2014, 4:12:03 AM · Difficulty 10.8065 · 6,301,110 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4a6e8575d54d1d9dfd2e25fafdbbb45543ba362ce59527d8bad512a4f2bfb0bf

View on Chainz ↗

Height

#502,052

Difficulty

10.806459

Transactions

Size

1.99 KB

Version

Bits

0ace741a

Nonce

15,103

Timestamp

4/20/2014, 4:12:03 AM

Confirmations

6,301,110

Mined by

⛏️ $RAeX2hokFQpmApFfNcLFPn3VUNCDqikhfHW

Merkle Root

f7bff9159c4650ee1ea9f9e8595614d0495415d5ed58a579e13d29c29610b50a

Transactions (4)

Coinbaseaa14b424ac767f…a0b3fdf60bbbcf

1 in → 18 out8.5800 XPM675 B

AeX2hokF…DqikhfHW AREQGaCC…V47D9Shh AX9beGKz…TMm6jM6X AGz9gyZW…bo8NYQpw AZr7Ptuw…CM4Yw5jq

0e56a1e1a9dc9a…190db60f98a643

1 in → 2 out8.5700 XPM226 B

ALwT2MzJ…BJNSW9zk ARkq9tY2…fDouQT3G

0c29f05e394bd5…160066167995e2

1 in → 2 out8.0691 XPM226 B

AM8GuxnN…AfjbhWoV ARiqh2Xp…3KtFTDiT

474767e68d015e…731ed27fa5455f

5 in → 2 out5.0202 XPM818 B

AZaKmj1Z…LeadwtuW Aeeodmp4…PDMjU7JD

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.

2.299 × 10¹⁰⁰(101-digit number)

22997965232535777637…51809248495106608119

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

2.299 × 10¹⁰⁰(101-digit number)

22997965232535777637…51809248495106608119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.299 × 10¹⁰⁰(101-digit number)

22997965232535777637…51809248495106608121

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

4.599 × 10¹⁰⁰(101-digit number)

45995930465071555274…03618496990213216239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.599 × 10¹⁰⁰(101-digit number)

45995930465071555274…03618496990213216241

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

9.199 × 10¹⁰⁰(101-digit number)

91991860930143110549…07236993980426432479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.199 × 10¹⁰⁰(101-digit number)

91991860930143110549…07236993980426432481

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

1.839 × 10¹⁰¹(102-digit number)

18398372186028622109…14473987960852864959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.839 × 10¹⁰¹(102-digit number)

18398372186028622109…14473987960852864961

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

3.679 × 10¹⁰¹(102-digit number)

36796744372057244219…28947975921705729919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.679 × 10¹⁰¹(102-digit number)

36796744372057244219…28947975921705729921

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