Block #354,278

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/11/2014, 11:06:53 AM · Difficulty 10.3394 · 6,458,260 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

98313126b998a8c0d65d82aa34c3798e2a1b09a2f421c920fe7ddfa75c15202b

View on Chainz ↗

Height

#354,278

Difficulty

10.339417

Transactions

Size

572 B

Version

Bits

0a56e40e

Nonce

20,218

Timestamp

1/11/2014, 11:06:53 AM

Confirmations

6,458,260

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

ce21da5a162f965d13c8edeab33bd7f2715f53f0d3fc28bdafd0510af60caee7

Transactions (2)

Coinbase1fb74617690309…c3df472abf5f34

1 in → 1 out9.3500 XPM110 B

AeKNrjNj…1NEq95Ta

96b4b5948ac068…0974ca25450a46

2 in → 2 out6.2863 XPM373 B

AJ2ew3S7…EHPTaiPf AHeiEWH5…jcm1NKMM

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.

5.346 × 10⁹¹(92-digit number)

53465924662629958629…71552213953325662679

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

5.346 × 10⁹¹(92-digit number)

53465924662629958629…71552213953325662679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.346 × 10⁹¹(92-digit number)

53465924662629958629…71552213953325662681

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

1.069 × 10⁹²(93-digit number)

10693184932525991725…43104427906651325359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.069 × 10⁹²(93-digit number)

10693184932525991725…43104427906651325361

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

2.138 × 10⁹²(93-digit number)

21386369865051983451…86208855813302650719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.138 × 10⁹²(93-digit number)

21386369865051983451…86208855813302650721

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

4.277 × 10⁹²(93-digit number)

42772739730103966903…72417711626605301439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.277 × 10⁹²(93-digit number)

42772739730103966903…72417711626605301441

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

8.554 × 10⁹²(93-digit number)

85545479460207933807…44835423253210602879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.554 × 10⁹²(93-digit number)

85545479460207933807…44835423253210602881

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 #354,278

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