Block #790,873

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/31/2014, 3:32:54 PM · Difficulty 10.9733 · 6,008,703 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7bc3334def3e8274f70471db0dbf632f0add6046b1f4c16a6ff45eeefc181104

View on Chainz ↗

Height

#790,873

Difficulty

10.973294

Transactions

Size

1.23 KB

Version

Bits

0af929c9

Nonce

2,847,826,576

Timestamp

10/31/2014, 3:32:54 PM

Confirmations

6,008,703

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

a729d85cb6703c6dbbf47028efa4e72adb30cf9767e95b60e562b2d71de10c69

Transactions (5)

Coinbase35d6e2d0b810dd…849488e7fd989b

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

fcff5a21dc2f22…43c83738adad83

2 in → 2 out14.5640 XPM374 B

AWLEzuk2…jBHYrf3R ALGi8LoD…G3qDCeNb

830107aa15f474…a56889a2434325

1 in → 2 out7.6942 XPM225 B

AKUvR6c6…PjpFWiw2 AWNhZ537…cRBUpqfV

5318bdcb29f1c2…762d37215c2028

1 in → 2 out6.4980 XPM225 B

ALWAPFSP…zxt3sEzR AREmLC5L…3hsWg33i

e757fb827d2107…53e59977fc3df0

1 in → 2 out7.2545 XPM227 B

AGdWVjRk…LFVsqCnK AbTPVs9S…hi19YacD

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.

8.432 × 10⁹⁴(95-digit number)

84320676297042581160…70838456982893537139

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

8.432 × 10⁹⁴(95-digit number)

84320676297042581160…70838456982893537139

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.432 × 10⁹⁴(95-digit number)

84320676297042581160…70838456982893537141

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

1.686 × 10⁹⁵(96-digit number)

16864135259408516232…41676913965787074279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.686 × 10⁹⁵(96-digit number)

16864135259408516232…41676913965787074281

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

3.372 × 10⁹⁵(96-digit number)

33728270518817032464…83353827931574148559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.372 × 10⁹⁵(96-digit number)

33728270518817032464…83353827931574148561

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

6.745 × 10⁹⁵(96-digit number)

67456541037634064928…66707655863148297119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.745 × 10⁹⁵(96-digit number)

67456541037634064928…66707655863148297121

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

1.349 × 10⁹⁶(97-digit number)

13491308207526812985…33415311726296594239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.349 × 10⁹⁶(97-digit number)

13491308207526812985…33415311726296594241

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