Block #130,413

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/23/2013, 1:55:21 PM · Difficulty 9.7853 · 6,659,482 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0a25ba1d76a6e94cd30a39cb592d2e4aa297dc7605272c6246838401119e192c

View on Chainz ↗

Height

#130,413

Difficulty

9.785334

Transactions

Size

393 B

Version

Bits

09c90bae

Nonce

78,995

Timestamp

8/23/2013, 1:55:21 PM

Confirmations

6,659,482

Merkle Root

f0a63ec8669b414c587941a753496e0c7d2e1e2af360bb9a44a6fc80a2fb81b2

Transactions (2)

Coinbase8f72517114a403…35454f309b32cd

1 in → 1 out10.4400 XPM109 B

AUto6Gg8…kZUKUEoK

c379dcf8a6eb4b…1421bf5a5efc1e

1 in → 1 out2.0146 XPM193 B

APBxWs9R…KTHWo3fT

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.

4.506 × 10⁹⁶(97-digit number)

45068891963287076882…23274171081722121549

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

4.506 × 10⁹⁶(97-digit number)

45068891963287076882…23274171081722121549

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.506 × 10⁹⁶(97-digit number)

45068891963287076882…23274171081722121551

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

9.013 × 10⁹⁶(97-digit number)

90137783926574153765…46548342163444243099

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.013 × 10⁹⁶(97-digit number)

90137783926574153765…46548342163444243101

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

1.802 × 10⁹⁷(98-digit number)

18027556785314830753…93096684326888486199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.802 × 10⁹⁷(98-digit number)

18027556785314830753…93096684326888486201

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

3.605 × 10⁹⁷(98-digit number)

36055113570629661506…86193368653776972399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.605 × 10⁹⁷(98-digit number)

36055113570629661506…86193368653776972401

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

7.211 × 10⁹⁷(98-digit number)

72110227141259323012…72386737307553944799

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