Block #374,467

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/25/2014, 1:17:22 AM · Difficulty 10.4229 · 6,429,286 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bf3e17c98d4c832951b7d8dab39ec29778217ac971fe8cc390ca68ba2d6c4346

View on Chainz ↗

Height

#374,467

Difficulty

10.422864

Transactions

Size

3.93 KB

Version

Bits

0a6c40d5

Nonce

37,793

Timestamp

1/25/2014, 1:17:22 AM

Confirmations

6,429,286

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

79227a0466bf35d111239fa986cd256ee10d82780ae6f6e1e1ff26e9c5ada67d

Transactions (3)

Coinbase98019c772fbc12…0c0811d13e273f

1 in → 1 out9.2400 XPM116 B

AbwWkWZt…kawDhufa

c4356f3afea139…058341a21029f3

2 in → 7 out19.1900 XPM477 B

AVnfbCeS…wU5T1Pkc AXw6mEKq…fKqEjtEj AeKNrjNj…1NEq95Ta AVzzPjcq…AQ7ny896 ANTGMD8n…pvc8NoeL

6bb8fb0bac6587…8f5328bf1b2e1f

22 in → 2 out22.9419 XPM3.26 KB

AZaKpimA…TaFCXjLt AbYoLR1Q…tcYrembK

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.

1.912 × 10⁹⁹(100-digit number)

19127285575175608163…81696764682094885979

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

1.912 × 10⁹⁹(100-digit number)

19127285575175608163…81696764682094885979

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.912 × 10⁹⁹(100-digit number)

19127285575175608163…81696764682094885981

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

3.825 × 10⁹⁹(100-digit number)

38254571150351216326…63393529364189771959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.825 × 10⁹⁹(100-digit number)

38254571150351216326…63393529364189771961

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

7.650 × 10⁹⁹(100-digit number)

76509142300702432652…26787058728379543919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.650 × 10⁹⁹(100-digit number)

76509142300702432652…26787058728379543921

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

1.530 × 10¹⁰⁰(101-digit number)

15301828460140486530…53574117456759087839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.530 × 10¹⁰⁰(101-digit number)

15301828460140486530…53574117456759087841

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

3.060 × 10¹⁰⁰(101-digit number)

30603656920280973061…07148234913518175679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.060 × 10¹⁰⁰(101-digit number)

30603656920280973061…07148234913518175681

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