Block #303,090

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/10/2013, 4:44:36 AM · Difficulty 9.9929 · 6,504,253 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ea5b7b020a81d4aefb3ba542e022f772a480290c3f34842de2a2a8422c15402d

View on Chainz ↗

Height

#303,090

Difficulty

9.992895

Transactions

Size

2.46 KB

Version

Bits

09fe2e5c

Nonce

19,148

Timestamp

12/10/2013, 4:44:36 AM

Confirmations

6,504,253

Mined by

⛏️ aRAHfwsMTbKqm7xANXirE2h6zzLEpY1MpjeT

Merkle Root

6b37e6ae4d67a056c8ccd961d55e0da19356eb4cb881e6e2ada9296732a2ad16

Transactions (4)

Coinbasef55d679dd90749…371bdfaf090227

1 in → 29 out9.9800 XPM1.02 KB

AHfwsMTb…pY1MpjeT ANxP1eAn…px9y56pB AYJ68rmN…zHKL2WMU AcM3ext6…Hwtj9Qp3 AG8UzQTL…AeALjTXg

d6f74c3daf8423…c6f692860baa37

3 in → 2 out25.6474 XPM521 B

AGYyeRec…5tDHVPnz AWs79Xej…SzYZaAT2

408416e6390c16…0f7f101c6fc401

3 in → 1 out45.1340 XPM487 B

AJDnzH8y…vr5iVSZ6

d83cd08aa8da3a…700cbf896692c9

2 in → 2 out11.7638 XPM374 B

AUqvBPoR…GkMANmTc AKc2zo7j…PxUhcLd3

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.

5.830 × 10⁹⁶(97-digit number)

58300322304652398523…06140056817212176639

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

5.830 × 10⁹⁶(97-digit number)

58300322304652398523…06140056817212176639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.830 × 10⁹⁶(97-digit number)

58300322304652398523…06140056817212176641

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

1.166 × 10⁹⁷(98-digit number)

11660064460930479704…12280113634424353279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.166 × 10⁹⁷(98-digit number)

11660064460930479704…12280113634424353281

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

2.332 × 10⁹⁷(98-digit number)

23320128921860959409…24560227268848706559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.332 × 10⁹⁷(98-digit number)

23320128921860959409…24560227268848706561

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

4.664 × 10⁹⁷(98-digit number)

46640257843721918818…49120454537697413119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.664 × 10⁹⁷(98-digit number)

46640257843721918818…49120454537697413121

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

9.328 × 10⁹⁷(98-digit number)

93280515687443837637…98240909075394826239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.328 × 10⁹⁷(98-digit number)

93280515687443837637…98240909075394826241

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 #303,090

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