Block #875,905

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/30/2014, 11:06:45 PM · Difficulty 10.9652 · 5,923,164 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c4476019ae041e2a395ea7daea12279112a5eca408174cd5cf0f508d5b8508c9

View on Chainz ↗

Height

#875,905

Difficulty

10.965217

Transactions

Size

889 B

Version

Bits

0af71876

Nonce

205,965

Timestamp

12/30/2014, 11:06:45 PM

Confirmations

5,923,164

Mined by

⛏️ aT1OAXz2kWvXMhDXBmF1MPgL7ZtTCLV5ZFCDBd

Merkle Root

ab338d34346cad78511655823240efa057b4a64d5f720587578539bf65186eef

Transactions (2)

Coinbase5cb9b41bc0b470…18bfd0d2446a54

1 in → 15 out8.3000 XPM573 B

AXz2kWvX…V5ZFCDBd AJzWx2VD…j4ZSMit5 AGz9gyZW…bo8NYQpw AKF9hNmX…pjjmh9Dc AXRun4Jx…ReRaSdaU

7a7c4172f2e07d…99298648aef948

1 in → 2 out8.2900 XPM226 B

ALE5K4pq…7ijXiNtt AYrwBKyU…1S6w2wRP

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.

9.889 × 10⁹³(94-digit number)

98898425007960053239…69264761177456537359

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

9.889 × 10⁹³(94-digit number)

98898425007960053239…69264761177456537359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.889 × 10⁹³(94-digit number)

98898425007960053239…69264761177456537361

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

1.977 × 10⁹⁴(95-digit number)

19779685001592010647…38529522354913074719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.977 × 10⁹⁴(95-digit number)

19779685001592010647…38529522354913074721

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

3.955 × 10⁹⁴(95-digit number)

39559370003184021295…77059044709826149439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.955 × 10⁹⁴(95-digit number)

39559370003184021295…77059044709826149441

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

7.911 × 10⁹⁴(95-digit number)

79118740006368042591…54118089419652298879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.911 × 10⁹⁴(95-digit number)

79118740006368042591…54118089419652298881

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

1.582 × 10⁹⁵(96-digit number)

15823748001273608518…08236178839304597759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.582 × 10⁹⁵(96-digit number)

15823748001273608518…08236178839304597761

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

3.164 × 10⁹⁵(96-digit number)

31647496002547217036…16472357678609195519

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