Block #775,014

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/19/2014, 4:11:38 AM · Difficulty 10.9820 · 6,019,318 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

832be2caf7ab0ead9a5ff488c5e09a3aefd7c9546621721b5ed22ce109c4cb2c

View on Chainz ↗

Height

#775,014

Difficulty

10.981978

Transactions

Size

629 B

Version

Bits

0afb62f0

Nonce

28,311

Timestamp

10/19/2014, 4:11:38 AM

Confirmations

6,019,318

Merkle Root

74a2be2e4adcb0d1b09e22965b664375ea2c988cf6880c10c84520b8256a2144

Transactions (1)

Coinbase74a2be2e4adcb0…4520b8256a2144

1 in → 14 out8.2783 XPM539 B

AXz2kWvX…V5ZFCDBd AaHhfFDZ…aDX1zc2i AJzWx2VD…j4ZSMit5 APfZjrNu…Wvzt6AFp AGz9gyZW…bo8NYQpw

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.

8.513 × 10⁹³(94-digit number)

85139949462791609639…87500850489635324799

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

8.513 × 10⁹³(94-digit number)

85139949462791609639…87500850489635324799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.513 × 10⁹³(94-digit number)

85139949462791609639…87500850489635324801

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

1.702 × 10⁹⁴(95-digit number)

17027989892558321927…75001700979270649599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.702 × 10⁹⁴(95-digit number)

17027989892558321927…75001700979270649601

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

3.405 × 10⁹⁴(95-digit number)

34055979785116643855…50003401958541299199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.405 × 10⁹⁴(95-digit number)

34055979785116643855…50003401958541299201

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

6.811 × 10⁹⁴(95-digit number)

68111959570233287711…00006803917082598399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.811 × 10⁹⁴(95-digit number)

68111959570233287711…00006803917082598401

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

1.362 × 10⁹⁵(96-digit number)

13622391914046657542…00013607834165196799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.362 × 10⁹⁵(96-digit number)

13622391914046657542…00013607834165196801

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

2.724 × 10⁹⁵(96-digit number)

27244783828093315084…00027215668330393599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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