Block #528,239

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/6/2014, 1:04:12 PM · Difficulty 10.8861 · 6,281,530 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

434184c37c8b937ec75948d2f1437adda98aa05556d48f852d93b2eeb0fce77f

View on Chainz ↗

Height

#528,239

Difficulty

10.886061

Transactions

Size

1.39 KB

Version

Bits

0ae2d4eb

Nonce

32,997,244

Timestamp

5/6/2014, 1:04:12 PM

Confirmations

6,281,530

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e2ec720924d28f814d8b5ca13a1612c03101344aa7b301e096e2ee990e3b7a79

Transactions (2)

Coinbasef182352016ab59…645e4f22b810b2

1 in → 1 out8.4400 XPM116 B

ANSXnLY2…Sd25TjkD

d06b4a81c54163…d9a868a4b34f6b

4 in → 18 out19.6535 XPM1.19 KB

AKfwEQcv…uF2f3oRH AJRwGPSP…QDRWdi2B AG3aRtpm…tTwZ6xx6 Ae4Lc5yt…Zvwdfk4k AaVFHFSq…bCnX1Bpw

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.

1.983 × 10¹⁰⁰(101-digit number)

19830093635646237786…32755173614443194239

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

1.983 × 10¹⁰⁰(101-digit number)

19830093635646237786…32755173614443194239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.983 × 10¹⁰⁰(101-digit number)

19830093635646237786…32755173614443194241

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

3.966 × 10¹⁰⁰(101-digit number)

39660187271292475572…65510347228886388479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.966 × 10¹⁰⁰(101-digit number)

39660187271292475572…65510347228886388481

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

7.932 × 10¹⁰⁰(101-digit number)

79320374542584951145…31020694457772776959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.932 × 10¹⁰⁰(101-digit number)

79320374542584951145…31020694457772776961

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

1.586 × 10¹⁰¹(102-digit number)

15864074908516990229…62041388915545553919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.586 × 10¹⁰¹(102-digit number)

15864074908516990229…62041388915545553921

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

3.172 × 10¹⁰¹(102-digit number)

31728149817033980458…24082777831091107839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.172 × 10¹⁰¹(102-digit number)

31728149817033980458…24082777831091107841

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 #528,239

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