Block #210,442

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/15/2013, 3:37:14 AM · Difficulty 9.9130 · 6,606,434 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

691ea3000298cc1d58fdb893cd5e2d69dc93deeb771fc22d1190e4201848771a

View on Chainz ↗

Height

#210,442

Difficulty

9.913000

Transactions

Size

1.44 KB

Version

Bits

09e9ba5a

Nonce

298,748

Timestamp

10/15/2013, 3:37:14 AM

Confirmations

6,606,434

Mined by

⛏️ P2SHAbuU1HhSi58QcdzhwKqhpJiRG3JPwsJEbB

Merkle Root

4152c430637d34c67ccfb571e5075169b796fcc32c68fe99f38f27c3db3a43a4

Transactions (4)

Coinbase95558e53dab9e5…1d85a013664a09

1 in → 1 out10.1900 XPM110 B

AbuU1HhS…JPwsJEbB

eb82bc6c27738e…190362a24d83ac

2 in → 2 out150.0138 XPM373 B

ALtdsLXa…MKpYxF6f AXCUrkb8…Sidrn3pu

bb7f146d78e82c…a948015f2993aa

2 in → 2 out20.0101 XPM375 B

AdtGRWCH…Bc4dedM7 AKFM8FUF…xx7TmBCN

e0b11182c4b8f1…bf12f90f9ef9b6

3 in → 2 out4.5717 XPM522 B

AUwKMCYC…hHVVSiWv ANmQZvKZ…8YsAf3zd

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.

1.536 × 10⁹⁵(96-digit number)

15366842827913664688…33786632325427722239

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

1.536 × 10⁹⁵(96-digit number)

15366842827913664688…33786632325427722239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.536 × 10⁹⁵(96-digit number)

15366842827913664688…33786632325427722241

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

3.073 × 10⁹⁵(96-digit number)

30733685655827329377…67573264650855444479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.073 × 10⁹⁵(96-digit number)

30733685655827329377…67573264650855444481

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

6.146 × 10⁹⁵(96-digit number)

61467371311654658754…35146529301710888959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.146 × 10⁹⁵(96-digit number)

61467371311654658754…35146529301710888961

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

1.229 × 10⁹⁶(97-digit number)

12293474262330931750…70293058603421777919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.229 × 10⁹⁶(97-digit number)

12293474262330931750…70293058603421777921

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

2.458 × 10⁹⁶(97-digit number)

24586948524661863501…40586117206843555839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.458 × 10⁹⁶(97-digit number)

24586948524661863501…40586117206843555841

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 #210,442

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