Block #231,364

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/28/2013, 9:59:19 AM · Difficulty 9.9403 · 6,572,658 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2a49217df32afdfc9401e3d0cd31ba1a4f9eea27e693eb2d1f18e0701e7f4f4e

View on Chainz ↗

Height

#231,364

Difficulty

9.940281

Transactions

Size

5.67 KB

Version

Bits

09f0b63c

Nonce

205,365

Timestamp

10/28/2013, 9:59:19 AM

Confirmations

6,572,658

Mined by

⛏️ P2SHAb7qzywW9CrR8MLf7aJXUww3uaq3niWUSQ

Merkle Root

d2ed7969ddffd0dc539f8ad0c57b81c65bf9fe8ab6721b56a11849e8a8598d62

Transactions (5)

Coinbased6efa6263f1919…b553c106680583

1 in → 1 out10.1900 XPM109 B

Ab7qzywW…q3niWUSQ

e32d0544980141…492dca4a0651f0

1 in → 2 out10.1000 XPM227 B

AX9At7E9…ueAX5FFV Ab3dSvM7…Qoxxb9tp

0caa005c1a2239…6fd635f11c3d87

1 in → 2 out10.1000 XPM225 B

AevGNETc…VNmszgdH AaVFHFSq…bCnX1Bpw

220cb40908d02f…5cd8032bb4b06c

33 in → 2 out95.9100 XPM4.85 KB

AJmg4wTN…c5r5YtRi AVDexfG7…kiHqkYov

162969f4fcee0c…cceff309debe6f

1 in → 1 out6.5425 XPM192 B

AK7byDmv…K3he4dUG

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.

4.389 × 10⁹³(94-digit number)

43893478893584880342…74814093020650566399

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

4.389 × 10⁹³(94-digit number)

43893478893584880342…74814093020650566399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.389 × 10⁹³(94-digit number)

43893478893584880342…74814093020650566401

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

8.778 × 10⁹³(94-digit number)

87786957787169760684…49628186041301132799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.778 × 10⁹³(94-digit number)

87786957787169760684…49628186041301132801

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

1.755 × 10⁹⁴(95-digit number)

17557391557433952136…99256372082602265599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.755 × 10⁹⁴(95-digit number)

17557391557433952136…99256372082602265601

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

3.511 × 10⁹⁴(95-digit number)

35114783114867904273…98512744165204531199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.511 × 10⁹⁴(95-digit number)

35114783114867904273…98512744165204531201

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

7.022 × 10⁹⁴(95-digit number)

70229566229735808547…97025488330409062399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.022 × 10⁹⁴(95-digit number)

70229566229735808547…97025488330409062401

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