Block #298,910

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/7/2013, 3:10:51 PM · Difficulty 9.9920 · 6,515,981 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1bbb5e878aebb65e6941e0349c25c20c3f8605e3d6a06c4edee948c9c5593ac0

View on Chainz ↗

Height

#298,910

Difficulty

9.992037

Transactions

Size

1.18 KB

Version

Bits

09fdf61e

Nonce

212,720

Timestamp

12/7/2013, 3:10:51 PM

Confirmations

6,515,981

Mined by

⛏️ aR:+AHuJ9wYhTJUvyVGtJfHi8VJT6eBGmgHrKZ

Merkle Root

3be6bb8e5d5e2956254043d67006eb476334362d8d1d7f2b9e84c4bf909bc019

Transactions (1)

Coinbase3be6bb8e5d5e29…84c4bf909bc019

1 in → 31 out9.9800 XPM1.09 KB

AHuJ9wYh…BGmgHrKZ Acskt6D1…Db4ci1L8 AX2fAveb…zoLMVBZ4 AN8nUzff…YcDfRDQ2 AJzWx2VD…j4ZSMit5

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.

6.146 × 10⁹⁶(97-digit number)

61465096486720289455…33445592328998618919

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

6.146 × 10⁹⁶(97-digit number)

61465096486720289455…33445592328998618919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.146 × 10⁹⁶(97-digit number)

61465096486720289455…33445592328998618921

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

1.229 × 10⁹⁷(98-digit number)

12293019297344057891…66891184657997237839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.229 × 10⁹⁷(98-digit number)

12293019297344057891…66891184657997237841

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

2.458 × 10⁹⁷(98-digit number)

24586038594688115782…33782369315994475679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.458 × 10⁹⁷(98-digit number)

24586038594688115782…33782369315994475681

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

4.917 × 10⁹⁷(98-digit number)

49172077189376231564…67564738631988951359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.917 × 10⁹⁷(98-digit number)

49172077189376231564…67564738631988951361

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

9.834 × 10⁹⁷(98-digit number)

98344154378752463128…35129477263977902719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.834 × 10⁹⁷(98-digit number)

98344154378752463128…35129477263977902721

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 #298,910

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