Block #292,477

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/3/2013, 6:29:39 PM · Difficulty 9.9903 · 6,502,581 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2809ef6d84f570a0820ae29d9b8fc70995a75a1de12023358eb3bd7c57d3c3a8

View on Chainz ↗

Height

#292,477

Difficulty

9.990303

Transactions

Size

1.95 KB

Version

Bits

09fd8483

Nonce

258,954

Timestamp

12/3/2013, 6:29:39 PM

Confirmations

6,502,581

Mined by

⛏️ }vaR"ANuKx9Kemb4q2j6b7vjmfuKrAuwm7nrBRq

Merkle Root

22310301756a9a247b4e4b2322760ebf24682445bb8983d18c3c942c7eea14be

Transactions (4)

Coinbase8f60a31de37144…231c78befcfef3

1 in → 30 out9.9800 XPM1.06 KB

ANuKx9Ke…wm7nrBRq AGPYJBwg…5yWMRKmU APfZjrNu…Wvzt6AFp AMttQDuf…7j6tfS9x AL2bBFB3…zSrryXUN

976df451c31367…01022090be5ab6

1 in → 2 out2.6482 XPM226 B

AdPcVVNt…Q6t6NVov ATruZC4X…BKxHqi3c

b3619453c32f02…a38c05089190e8

1 in → 2 out1.7532 XPM226 B

AcQzCeYG…omBu4E9k AKmxBBzd…AHmu4uiE

bbdc9c325d8d05…fc3d161e5df7f2

2 in → 2 out1.1130 XPM374 B

ATYAh5sL…QS5N8Qfp Acake8Rn…rXn5FsEu

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.

3.470 × 10⁹⁵(96-digit number)

34707572205680189034…65919802740709898239

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

3.470 × 10⁹⁵(96-digit number)

34707572205680189034…65919802740709898239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.470 × 10⁹⁵(96-digit number)

34707572205680189034…65919802740709898241

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

6.941 × 10⁹⁵(96-digit number)

69415144411360378069…31839605481419796479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.941 × 10⁹⁵(96-digit number)

69415144411360378069…31839605481419796481

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

1.388 × 10⁹⁶(97-digit number)

13883028882272075613…63679210962839592959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.388 × 10⁹⁶(97-digit number)

13883028882272075613…63679210962839592961

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

2.776 × 10⁹⁶(97-digit number)

27766057764544151227…27358421925679185919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.776 × 10⁹⁶(97-digit number)

27766057764544151227…27358421925679185921

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

5.553 × 10⁹⁶(97-digit number)

55532115529088302455…54716843851358371839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.553 × 10⁹⁶(97-digit number)

55532115529088302455…54716843851358371841

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