Block #143,359

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/31/2013, 2:31:29 PM · Difficulty 9.8375 · 6,671,063 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c76e6adb207db9edc4f360de7092975e4ec0b92efb93fe1294c6f0543edea07c

View on Chainz ↗

Height

#143,359

Difficulty

9.837523

Transactions

Size

1.66 KB

Version

Bits

09d667e4

Nonce

22,591

Timestamp

8/31/2013, 2:31:29 PM

Confirmations

6,671,063

Mined by

⛏️ P2SHAHmvhRqWL5g4Fhy2RMfdSpypuGqgG5FwBR

Merkle Root

80ac276303819b2dd78309b336c72ac92508a39a26638b530559134d8e7ae1f8

Transactions (5)

Coinbase7c419b89634bbb…254102c377a82e

1 in → 1 out10.3600 XPM109 B

AHmvhRqW…qgG5FwBR

e0a9981ccc4a64…41d2813906e3a9

8 in → 1 out83.9800 XPM956 B

AK9hFuSp…me32gPyq

5e39eeef2c619e…8ed0519c04bab5

1 in → 1 out10.3200 XPM159 B

AGjPFuk8…G8AukLLa

539e90be35a260…c4527275974033

1 in → 2 out10.3400 XPM193 B

AUjpb4B2…zAKTW5cs AaMRUFMG…S11BNFrC

4cecfd38222cc1…294d4989a5fb53

1 in → 1 out5.1650 XPM192 B

AeguK5Ai…CLUqoF9q

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.

1.697 × 10⁹⁴(95-digit number)

16970941961852947440…19093210593839747599

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

1.697 × 10⁹⁴(95-digit number)

16970941961852947440…19093210593839747599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.697 × 10⁹⁴(95-digit number)

16970941961852947440…19093210593839747601

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

3.394 × 10⁹⁴(95-digit number)

33941883923705894881…38186421187679495199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.394 × 10⁹⁴(95-digit number)

33941883923705894881…38186421187679495201

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

6.788 × 10⁹⁴(95-digit number)

67883767847411789763…76372842375358990399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.788 × 10⁹⁴(95-digit number)

67883767847411789763…76372842375358990401

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

1.357 × 10⁹⁵(96-digit number)

13576753569482357952…52745684750717980799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.357 × 10⁹⁵(96-digit number)

13576753569482357952…52745684750717980801

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

2.715 × 10⁹⁵(96-digit number)

27153507138964715905…05491369501435961599

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

Block #143,359

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