Block #246,300

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/6/2013, 12:50:55 AM · Difficulty 9.9644 · 6,552,061 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

46f510004d129c158bf792808b5f7020786c029bacda8476f11aee453c48baf4

View on Chainz ↗

Height

#246,300

Difficulty

9.964364

Transactions

Size

1.41 KB

Version

Bits

09f6e08f

Nonce

492

Timestamp

11/6/2013, 12:50:55 AM

Confirmations

6,552,061

Mined by

⛏️ P2SHAZDUEbdSvp8cw8AAZ1fERZUqSYRYKMRZET

Merkle Root

a9388faae69a42e3603539c337fa0c07fb7e8ea107ed31d4f7a6d504dc2237b9

Transactions (5)

Coinbase07cfeacdade0ed…733a4a0c413482

1 in → 2 out10.1000 XPM137 B

AZDUEbdS…RYKMRZET ALfEGCwh…VawujfMm

4d53aed956d79c…6d424a72ed13e4

2 in → 2 out149.9091 XPM373 B

AYmzdtJB…hiasyn2t ARUshccM…CPuTAGcF

61088da7981872…23e1f6cb622e26

1 in → 1 out1133.2232 XPM192 B

AMorKomM…rqUQftkn

32f24538beeb87…2b04b0c778a7cb

2 in → 1 out20.1600 XPM273 B

ATN5ko6m…UbqfVBsa

4363ccc1bd3129…0514f022d1e100

2 in → 2 out0.1918 XPM374 B

AZ28uDvK…f3twk84z AM4DUx4F…6EcjKqgF

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.

4.800 × 10⁹⁹(100-digit number)

48003121458876043298…83301691627087575999

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

4.800 × 10⁹⁹(100-digit number)

48003121458876043298…83301691627087575999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.800 × 10⁹⁹(100-digit number)

48003121458876043298…83301691627087576001

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

9.600 × 10⁹⁹(100-digit number)

96006242917752086596…66603383254175151999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.600 × 10⁹⁹(100-digit number)

96006242917752086596…66603383254175152001

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

1.920 × 10¹⁰⁰(101-digit number)

19201248583550417319…33206766508350303999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.920 × 10¹⁰⁰(101-digit number)

19201248583550417319…33206766508350304001

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

3.840 × 10¹⁰⁰(101-digit number)

38402497167100834638…66413533016700607999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.840 × 10¹⁰⁰(101-digit number)

38402497167100834638…66413533016700608001

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

7.680 × 10¹⁰⁰(101-digit number)

76804994334201669276…32827066033401215999

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