Block #730,846

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/20/2014, 4:07:25 AM · Difficulty 10.9693 · 6,075,331 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1a81f0736cb4b4a2a9f16e525efedb47aec3c04e623c4af5a18dd56dad961ea9

View on Chainz ↗

Height

#730,846

Difficulty

10.969255

Transactions

Size

1.04 KB

Version

Bits

0af8211d

Nonce

829,660,238

Timestamp

9/20/2014, 4:07:25 AM

Confirmations

6,075,331

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e5621dc96f7c15e1f473540b8339357175943cdd7b6aad1e4386fa7a1d2af5b6

Transactions (4)

Coinbase65b3a179636fd4…569210749f7316

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

a5836f1c455c80…ad4eacb1552672

1 in → 2 out8.3000 XPM227 B

AH9Guk9b…jCeGxLQ4 AaF1rWqu…rpTE5LwQ

1b982978b54428…4230563475f636

1 in → 4 out8.3000 XPM261 B

ANFpe7j9…DDEt116M AeKNrjNj…1NEq95Ta AVMRAzar…3e1KTuWa AJcmFad4…YNAMFS3w

370fd7051ab2fe…a31e287865064b

2 in → 2 out5.5230 XPM373 B

AYuXtsY9…7h3id98y AVPGBrtu…hvKQjxQS

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.

4.529 × 10⁹⁷(98-digit number)

45294570279583809973…68394050689429667839

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

4.529 × 10⁹⁷(98-digit number)

45294570279583809973…68394050689429667839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.529 × 10⁹⁷(98-digit number)

45294570279583809973…68394050689429667841

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

9.058 × 10⁹⁷(98-digit number)

90589140559167619946…36788101378859335679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.058 × 10⁹⁷(98-digit number)

90589140559167619946…36788101378859335681

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

1.811 × 10⁹⁸(99-digit number)

18117828111833523989…73576202757718671359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.811 × 10⁹⁸(99-digit number)

18117828111833523989…73576202757718671361

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

3.623 × 10⁹⁸(99-digit number)

36235656223667047978…47152405515437342719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.623 × 10⁹⁸(99-digit number)

36235656223667047978…47152405515437342721

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

7.247 × 10⁹⁸(99-digit number)

72471312447334095957…94304811030874685439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.247 × 10⁹⁸(99-digit number)

72471312447334095957…94304811030874685441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.449 × 10⁹⁹(100-digit number)

14494262489466819191…88609622061749370879

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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