Block #534,572

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/10/2014, 9:58:49 AM · Difficulty 10.9022 · 6,275,873 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6e9cb2b43a878c5c65dc8ae5eb153cfaa086bd64792103174929e54888b030e4

View on Chainz ↗

Height

#534,572

Difficulty

10.902226

Transactions

Size

1.95 KB

Version

Bits

0ae6f847

Nonce

3,723,164

Timestamp

5/10/2014, 9:58:49 AM

Confirmations

6,275,873

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ccb3d63772a0eda8a0bf1f8278736a5e8145c2cd8d82016030813ae08ee5f086

Transactions (3)

Coinbaseb1764c3a1efa01…2b15b1de625a5b

1 in → 1 out8.4300 XPM116 B

ANSXnLY2…Sd25TjkD

8c7dca76813adb…c37b46056eb1c9

10 in → 2 out30.1524 XPM1.52 KB

ATWphLZp…qA85v9vh ALugLp5d…AoL5HyGB

535635dc4b10a2…6ce3cce6e3b127

1 in → 2 out6.7711 XPM226 B

AWVL1nZH…JUKcTJnA AG8u7ddV…cU5QJSqk

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.

1.937 × 10¹⁰⁰(101-digit number)

19379205822923414149…05533871191225710079

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

1.937 × 10¹⁰⁰(101-digit number)

19379205822923414149…05533871191225710079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.937 × 10¹⁰⁰(101-digit number)

19379205822923414149…05533871191225710081

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

3.875 × 10¹⁰⁰(101-digit number)

38758411645846828298…11067742382451420159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.875 × 10¹⁰⁰(101-digit number)

38758411645846828298…11067742382451420161

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

7.751 × 10¹⁰⁰(101-digit number)

77516823291693656597…22135484764902840319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.751 × 10¹⁰⁰(101-digit number)

77516823291693656597…22135484764902840321

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

1.550 × 10¹⁰¹(102-digit number)

15503364658338731319…44270969529805680639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.550 × 10¹⁰¹(102-digit number)

15503364658338731319…44270969529805680641

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

3.100 × 10¹⁰¹(102-digit number)

31006729316677462638…88541939059611361279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.100 × 10¹⁰¹(102-digit number)

31006729316677462638…88541939059611361281

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 #534,572

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