Block #300,873

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/8/2013, 8:20:13 PM · Difficulty 9.9924 · 6,505,515 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

57a6b5f6cf155bc76cc088dcfeee7413ce1c5b80298c53a85aab9ae1831e641c

View on Chainz ↗

Height

#300,873

Difficulty

9.992430

Transactions

Size

877 B

Version

Bits

09fe0fe5

Nonce

8,726

Timestamp

12/8/2013, 8:20:13 PM

Confirmations

6,505,515

Mined by

⛏️ P2SHAeGjBGD6Czx9a7yREZWxQ8WrhwcZTrEmVn

Merkle Root

f066cd02663f1efd8a4afdbdc9e5e52e978d0b6a0a5384ad3f1347f2508f379d

Transactions (3)

Coinbaseb29c7fb74583bc…31a6212ff66af9

1 in → 1 out10.0200 XPM109 B

AeGjBGD6…cZTrEmVn

e17830826fa671…58cee881c142dc

3 in → 2 out49.8106 XPM521 B

ATJQwQCe…ZZts7knC AZjQXPnX…4wgdoT5o

4964eb3db73400…ae6dff6a35644a

1 in → 1 out10.0000 XPM158 B

AXhxNajJ…CLP12ZGm

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.

1.326 × 10⁹²(93-digit number)

13267036983655807213…01921267142938618879

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

1.326 × 10⁹²(93-digit number)

13267036983655807213…01921267142938618879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.326 × 10⁹²(93-digit number)

13267036983655807213…01921267142938618881

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

2.653 × 10⁹²(93-digit number)

26534073967311614427…03842534285877237759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.653 × 10⁹²(93-digit number)

26534073967311614427…03842534285877237761

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

5.306 × 10⁹²(93-digit number)

53068147934623228854…07685068571754475519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.306 × 10⁹²(93-digit number)

53068147934623228854…07685068571754475521

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

1.061 × 10⁹³(94-digit number)

10613629586924645770…15370137143508951039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.061 × 10⁹³(94-digit number)

10613629586924645770…15370137143508951041

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

2.122 × 10⁹³(94-digit number)

21227259173849291541…30740274287017902079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.122 × 10⁹³(94-digit number)

21227259173849291541…30740274287017902081

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #300,873

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