Block #502,873

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/20/2014, 5:20:08 PM · Difficulty 10.8079 · 6,303,307 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e0c2cb2bfe13b5c13cc5a946e07959451055fd6e3b25a50aec34dc9a8a5302b1

View on Chainz ↗

Height

#502,873

Difficulty

10.807937

Transactions

Size

1.30 KB

Version

Bits

0aced4f5

Nonce

4,000,011

Timestamp

4/20/2014, 5:20:08 PM

Confirmations

6,303,307

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

5fa0285b25c8ef2e81399ce99c35e8b5e4b1347133a7f9460417b80729119bb9

Transactions (4)

Coinbasee22526ee543c23…5dd4271a703673

1 in → 1 out8.5800 XPM116 B

AbwWkWZt…kawDhufa

0bfb790f147e98…ae48a867d09052

1 in → 2 out5.3432 XPM227 B

ALD1ki6c…MDWqwbLp AZTFuznF…R2kwetrV

aae7b1322172a1…66661d1b50360e

1 in → 2 out4.9597 XPM226 B

AKZ5RZTL…EU8xnSi5 AbbQSUUx…kWiY4Tyq

246dd5d60ab2e1…0b7a72fad0c8e4

4 in → 2 out1.0240 XPM670 B

AYyfzxw1…41CKcwF1 AH6EP5Xv…i3i6MXs7

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.

2.056 × 10⁹⁹(100-digit number)

20562039390771751999…33231411677582643199

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

2.056 × 10⁹⁹(100-digit number)

20562039390771751999…33231411677582643199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.056 × 10⁹⁹(100-digit number)

20562039390771751999…33231411677582643201

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

4.112 × 10⁹⁹(100-digit number)

41124078781543503999…66462823355165286399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.112 × 10⁹⁹(100-digit number)

41124078781543503999…66462823355165286401

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

8.224 × 10⁹⁹(100-digit number)

82248157563087007999…32925646710330572799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.224 × 10⁹⁹(100-digit number)

82248157563087007999…32925646710330572801

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

1.644 × 10¹⁰⁰(101-digit number)

16449631512617401599…65851293420661145599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.644 × 10¹⁰⁰(101-digit number)

16449631512617401599…65851293420661145601

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

3.289 × 10¹⁰⁰(101-digit number)

32899263025234803199…31702586841322291199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.289 × 10¹⁰⁰(101-digit number)

32899263025234803199…31702586841322291201

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