Block #920,088

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/2/2015, 5:22:30 PM · Difficulty 10.9184 · 5,873,211 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3080f506d669cf522bc8f1131a46a0bfa59bfdfa9378eb2d535ac18dfaff34e7

View on Chainz ↗

Height

#920,088

Difficulty

10.918430

Transactions

Size

37.34 KB

Version

Bits

0aeb1e35

Nonce

389,040,937

Timestamp

2/2/2015, 5:22:30 PM

Confirmations

5,873,211

Merkle Root

ea545cd22a47999b6d4276cf1d96e88bef93fd98324dc003b22bee74bba3daef

Transactions (5)

Coinbase43c24f922de2b7…1540df0ba1976f

1 in → 1 out8.7900 XPM116 B

ANSXnLY2…Sd25TjkD

e0b8b270596de1…183dca3b63093f

1 in → 1 out2000.9900 XPM193 B

ARJftYX5…gsecibTb

1cb373b2ac3b72…ae8761d8c35c12

252 in → 2 out9500.3906 XPM36.51 KB

Adxt4qa2…1MqKKsEi AG4NaxaR…3SfZRkZN

89ef22bb036a76…8277bd76a1ed6c

1 in → 2 out4.3500 XPM226 B

AQSTJc1q…Db5ekdjR ALyoFbvZ…LWnZUvni

1ab0d0b9ce4118…94b677e61c75b5

1 in → 2 out4.3500 XPM226 B

AdGFnV3a…o6n2zX3x AaYNQy1f…ZSJfFasC

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.

1.938 × 10⁹⁶(97-digit number)

19380512554091620258…74775748603813651199

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

1.938 × 10⁹⁶(97-digit number)

19380512554091620258…74775748603813651199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.938 × 10⁹⁶(97-digit number)

19380512554091620258…74775748603813651201

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

3.876 × 10⁹⁶(97-digit number)

38761025108183240517…49551497207627302399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.876 × 10⁹⁶(97-digit number)

38761025108183240517…49551497207627302401

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

7.752 × 10⁹⁶(97-digit number)

77522050216366481035…99102994415254604799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.752 × 10⁹⁶(97-digit number)

77522050216366481035…99102994415254604801

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

1.550 × 10⁹⁷(98-digit number)

15504410043273296207…98205988830509209599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.550 × 10⁹⁷(98-digit number)

15504410043273296207…98205988830509209601

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

3.100 × 10⁹⁷(98-digit number)

31008820086546592414…96411977661018419199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.100 × 10⁹⁷(98-digit number)

31008820086546592414…96411977661018419201

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