Block #533,695

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/9/2014, 9:07:34 PM · Difficulty 10.9001 · 6,291,967 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5b435b40c8f465298390a38c0013c3ac60f46b98d8372b4f43f0a3b3265a6209

View on Chainz ↗

Height

#533,695

Difficulty

10.900103

Transactions

Size

1.45 KB

Version

Bits

0ae66d25

Nonce

46,847,537

Timestamp

5/9/2014, 9:07:34 PM

Confirmations

6,291,967

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

2d4b08b13d8c0a8cad0564e920091d10db9d3d35a79bf003848d7e63c679be14

Transactions (4)

Coinbaseb369cdd31fe9e4…53b7d9b86b1f3d

1 in → 1 out8.4400 XPM116 B

ANSXnLY2…Sd25TjkD

04d0bbfbc4947d…326929702f19d4

4 in → 2 out25.0431 XPM672 B

ASxxzo8K…TGWrKv8j AXDMmFGd…Y9Q64LFz

ae13ba3a184efd…a6873ca0528eeb

2 in → 2 out3.2959 XPM375 B

ALy7Ra4p…8KLmryJG AeKNrjNj…1NEq95Ta

3fa5f695fe259a…b1ba1532763438

1 in → 2 out0.7917 XPM226 B

AGdWVjRk…LFVsqCnK APUsSdvr…3m51ZUh2

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.

1.892 × 10¹⁰⁰(101-digit number)

18922474686592740743…14600415818886901759

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

1.892 × 10¹⁰⁰(101-digit number)

18922474686592740743…14600415818886901759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.892 × 10¹⁰⁰(101-digit number)

18922474686592740743…14600415818886901761

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

3.784 × 10¹⁰⁰(101-digit number)

37844949373185481487…29200831637773803519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.784 × 10¹⁰⁰(101-digit number)

37844949373185481487…29200831637773803521

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

7.568 × 10¹⁰⁰(101-digit number)

75689898746370962974…58401663275547607039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.568 × 10¹⁰⁰(101-digit number)

75689898746370962974…58401663275547607041

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

1.513 × 10¹⁰¹(102-digit number)

15137979749274192594…16803326551095214079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.513 × 10¹⁰¹(102-digit number)

15137979749274192594…16803326551095214081

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

3.027 × 10¹⁰¹(102-digit number)

30275959498548385189…33606653102190428159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.027 × 10¹⁰¹(102-digit number)

30275959498548385189…33606653102190428161

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 #533,695

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