Block #911,290

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/26/2015, 11:50:13 PM · Difficulty 10.9314 · 5,893,652 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6faed880ff997ebfe0db6eff5803fa96ba2e20dec2d45afbc16688ddc505846a

View on Chainz ↗

Height

#911,290

Difficulty

10.931422

Transactions

Size

2.00 KB

Version

Bits

0aee71b3

Nonce

409,952,148

Timestamp

1/26/2015, 11:50:13 PM

Confirmations

5,893,652

Mined by

⛏️ P2SHAGghSoAPbkD4oEWeJPhRr3XwpKaU6Nx4N9

Merkle Root

9124c95859de1fe6383e3dbd345f9678e20c2401556369a5edc584c5d24d5da1

Transactions (2)

Coinbase4086a5265299ad…1f11ab7cd47aa6

1 in → 1 out8.3900 XPM109 B

AGghSoAP…aU6Nx4N9

f0e13110cb22cb…a1afd2247077f9

12 in → 2 out997.9100 XPM1.81 KB

AQPm3VuJ…1xgjuFP1 AQ3SuyCM…AmNvneTb

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.

1.977 × 10⁹⁶(97-digit number)

19779135511615274071…62054929704765655039

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

1.977 × 10⁹⁶(97-digit number)

19779135511615274071…62054929704765655039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.977 × 10⁹⁶(97-digit number)

19779135511615274071…62054929704765655041

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

3.955 × 10⁹⁶(97-digit number)

39558271023230548143…24109859409531310079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.955 × 10⁹⁶(97-digit number)

39558271023230548143…24109859409531310081

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

7.911 × 10⁹⁶(97-digit number)

79116542046461096287…48219718819062620159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.911 × 10⁹⁶(97-digit number)

79116542046461096287…48219718819062620161

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

1.582 × 10⁹⁷(98-digit number)

15823308409292219257…96439437638125240319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.582 × 10⁹⁷(98-digit number)

15823308409292219257…96439437638125240321

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

3.164 × 10⁹⁷(98-digit number)

31646616818584438514…92878875276250480639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.164 × 10⁹⁷(98-digit number)

31646616818584438514…92878875276250480641

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