Block #146,406

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/2/2013, 12:00:56 PM · Difficulty 9.8475 · 6,649,543 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3ae7ae53a4bb34d6dae483d30a04338fb40b46da28450f3d3d358365b056c6f3

View on Chainz ↗

Height

#146,406

Difficulty

9.847539

Transactions

Size

925 B

Version

Bits

09d8f857

Nonce

39,831

Timestamp

9/2/2013, 12:00:56 PM

Confirmations

6,649,543

Mined by

⛏️ P2SHAJncPVjCK1u1yxn9MupH4uoY65dvbKtGE5

Merkle Root

270eba8773437433bcfa30c75136a4c66a2597a805a1053b50e3b5572c2de924

Transactions (3)

Coinbaseb2cd44df1e932f…b21a88eb0c7b16

1 in → 1 out10.3200 XPM109 B

AJncPVjC…dvbKtGE5

064923bc93c1e0…1fc419b9a8cd7b

1 in → 1 out10.3100 XPM159 B

Ae2P8tRG…ZBcRXaeZ

ddef30dc9c4866…1972b511387e85

4 in → 2 out31.0200 XPM569 B

ARWVvKkU…eP8yQmBx AFz9fXym…wh4UqpkL

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.

9.955 × 10⁸⁹(90-digit number)

99553833769789623055…15065501505034205759

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

9.955 × 10⁸⁹(90-digit number)

99553833769789623055…15065501505034205759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.955 × 10⁸⁹(90-digit number)

99553833769789623055…15065501505034205761

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

1.991 × 10⁹⁰(91-digit number)

19910766753957924611…30131003010068411519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.991 × 10⁹⁰(91-digit number)

19910766753957924611…30131003010068411521

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

3.982 × 10⁹⁰(91-digit number)

39821533507915849222…60262006020136823039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.982 × 10⁹⁰(91-digit number)

39821533507915849222…60262006020136823041

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

7.964 × 10⁹⁰(91-digit number)

79643067015831698444…20524012040273646079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.964 × 10⁹⁰(91-digit number)

79643067015831698444…20524012040273646081

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

1.592 × 10⁹¹(92-digit number)

15928613403166339688…41048024080547292159

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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