Block #812,443

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 11/15/2014, 5:03:15 PM · Difficulty 10.9734 · 5,996,701 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

694bd8dbf77f3959f9c103c2c8b60b72240c0f8d605e02278a07844981d88e3c

View on Chainz ↗

Height

#812,443

Difficulty

10.973370

Transactions

Size

1.67 KB

Version

Bits

0af92ec8

Nonce

1,516,425,568

Timestamp

11/15/2014, 5:03:15 PM

Confirmations

5,996,701

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

68d2145060f139232a964f98f66d65496680feba53164275ab7695ebfac8da36

Transactions (5)

Coinbaseb10f117987cb41…bef3b8977b47ec

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

09b5398cc69598…6e3bb635d1a5f2

5 in → 2 out31.1957 XPM819 B

ALT5Kgdc…x2HmLQYq AHZkUHtR…EUjZu7Tf

8a669d18d80d5c…ab2837ca265776

1 in → 2 out7.6548 XPM227 B

ALUjkiTP…c7dakN3v AWeFTqSF…usRDA3NM

2bbd8cf0cbb12f…0531a86d464896

1 in → 2 out7.5190 XPM226 B

Acibz2hH…4KK9AWqC APP6HhH3…dDS4LTzC

f6c69f6bdaa597…bcffc65aa23177

1 in → 2 out2.2051 XPM226 B

AcGL7NJd…XoCUQk8m ALGEpsmZ…rxksfAJd

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.

4.779 × 10⁹⁶(97-digit number)

47792708118956004458…80436882397299582079

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

4.779 × 10⁹⁶(97-digit number)

47792708118956004458…80436882397299582079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.779 × 10⁹⁶(97-digit number)

47792708118956004458…80436882397299582081

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

9.558 × 10⁹⁶(97-digit number)

95585416237912008916…60873764794599164159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.558 × 10⁹⁶(97-digit number)

95585416237912008916…60873764794599164161

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

1.911 × 10⁹⁷(98-digit number)

19117083247582401783…21747529589198328319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.911 × 10⁹⁷(98-digit number)

19117083247582401783…21747529589198328321

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

3.823 × 10⁹⁷(98-digit number)

38234166495164803566…43495059178396656639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.823 × 10⁹⁷(98-digit number)

38234166495164803566…43495059178396656641

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

7.646 × 10⁹⁷(98-digit number)

76468332990329607133…86990118356793313279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.646 × 10⁹⁷(98-digit number)

76468332990329607133…86990118356793313281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.529 × 10⁹⁸(99-digit number)

15293666598065921426…73980236713586626559

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

1.529 × 10⁹⁸(99-digit number)

15293666598065921426…73980236713586626561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 #812,443

Cookie Preferences