Block #433,456

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/7/2014, 2:36:41 PM · Difficulty 10.3437 · 6,375,297 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d187571ee333a1b28cfc3979bf2b45761fa669083ff369e0abba1e18219ccf41

View on Chainz ↗

Height

#433,456

Difficulty

10.343727

Transactions

Size

1.07 KB

Version

Bits

0a57fe85

Nonce

13,072

Timestamp

3/7/2014, 2:36:41 PM

Confirmations

6,375,297

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

384709ad46fec944aa0c5cf8aff61180e0e78f9fca07d78950d9a3dd855d204e

Transactions (3)

Coinbase775eccf0876370…af1433ab34d20f

1 in → 1 out9.3500 XPM116 B

AbwWkWZt…kawDhufa

58667e7d3fda48…ad81bb7856c9bb

3 in → 9 out28.0715 XPM658 B

AeKNrjNj…1NEq95Ta Ac7zuxVV…Vg7cSywn AVWB3Ybr…i5Z8mGNq AHSx1yai…YVKKVMzF AWtxvHFo…8goMQkVK

9555164825371c…74d3868fd8c99c

1 in → 2 out0.9900 XPM226 B

ATuu63n5…fBLgCofs AcFSBFBv…V7iHm3QP

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.

1.434 × 10⁹⁸(99-digit number)

14347150536109863068…92200431320749920279

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

1.434 × 10⁹⁸(99-digit number)

14347150536109863068…92200431320749920279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.434 × 10⁹⁸(99-digit number)

14347150536109863068…92200431320749920281

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

2.869 × 10⁹⁸(99-digit number)

28694301072219726137…84400862641499840559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.869 × 10⁹⁸(99-digit number)

28694301072219726137…84400862641499840561

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

5.738 × 10⁹⁸(99-digit number)

57388602144439452275…68801725282999681119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.738 × 10⁹⁸(99-digit number)

57388602144439452275…68801725282999681121

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

1.147 × 10⁹⁹(100-digit number)

11477720428887890455…37603450565999362239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.147 × 10⁹⁹(100-digit number)

11477720428887890455…37603450565999362241

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

2.295 × 10⁹⁹(100-digit number)

22955440857775780910…75206901131998724479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.295 × 10⁹⁹(100-digit number)

22955440857775780910…75206901131998724481

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 #433,456

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