Block #529,653

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/7/2014, 9:27:09 AM · Difficulty 10.8903 · 6,269,712 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

64087ea7d142f980aa6d5d8e9f91276ad761b3d971afd332fd1a7be7128f49ed

View on Chainz ↗

Height

#529,653

Difficulty

10.890320

Transactions

Size

1.08 KB

Version

Bits

0ae3ec01

Nonce

2,879,713

Timestamp

5/7/2014, 9:27:09 AM

Confirmations

6,269,712

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c4549c759710e61cc7578a37a6b810093f9e822557fbeac50fb82321f2890365

Transactions (5)

Coinbased05a0de48f5482…9b6f7252f31205

1 in → 1 out8.4600 XPM116 B

ANSXnLY2…Sd25TjkD

7c953df7c46ea5…bcd1e592234ff5

1 in → 2 out557.5828 XPM226 B

AZFBSVHN…x847KkUB AGdWVjRk…LFVsqCnK

bbafa8681fd933…0f9c1775087fb2

1 in → 2 out508.3652 XPM225 B

APPJkKKX…Pn9PnQB8 AXxii5R6…YQWb8263

3cb1ccafc009f8…3a35d7653f7ec0

1 in → 2 out254.5566 XPM225 B

AXkMWrT9…KvSPKK7L ALcKmmnm…2ew4L9se

81c2b88741a0eb…68c5bf03c0a5fe

1 in → 2 out5.4052 XPM225 B

AP3AMLKL…eNyMSmcj AeKNrjNj…1NEq95Ta

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.

1.169 × 10¹⁰⁰(101-digit number)

11693882736713745462…71192253940238660479

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

1.169 × 10¹⁰⁰(101-digit number)

11693882736713745462…71192253940238660479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.169 × 10¹⁰⁰(101-digit number)

11693882736713745462…71192253940238660481

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

2.338 × 10¹⁰⁰(101-digit number)

23387765473427490924…42384507880477320959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.338 × 10¹⁰⁰(101-digit number)

23387765473427490924…42384507880477320961

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

4.677 × 10¹⁰⁰(101-digit number)

46775530946854981848…84769015760954641919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.677 × 10¹⁰⁰(101-digit number)

46775530946854981848…84769015760954641921

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

9.355 × 10¹⁰⁰(101-digit number)

93551061893709963697…69538031521909283839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.355 × 10¹⁰⁰(101-digit number)

93551061893709963697…69538031521909283841

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

1.871 × 10¹⁰¹(102-digit number)

18710212378741992739…39076063043818567679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.871 × 10¹⁰¹(102-digit number)

18710212378741992739…39076063043818567681

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