Block #857,128

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/17/2014, 2:48:16 PM · Difficulty 10.9677 · 5,985,855 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

48793a2498f6e6d70c80f3506e465fe6c59a25d84d66cd0b1c7017bdd2052482

View on Chainz ↗

Height

#857,128

Difficulty

10.967659

Transactions

Size

1.04 KB

Version

Bits

0af7b883

Nonce

399,035,754

Timestamp

12/17/2014, 2:48:16 PM

Confirmations

5,985,855

Mined by

⛏️ P2SHAG1jnTu1ViMuyrDmMUyGwLWoziyqwBwLxS

Merkle Root

6416d62b2087da87939571056d4f8018d2745e5587e6907ce42de74d161fa06f

Transactions (5)

Coinbasea3d2b75aafac55…39b64c34a52d59

1 in → 1 out8.3550 XPM110 B

AG1jnTu1…yqwBwLxS

508a885cd5d939…00b5f52ad79bef

1 in → 1 out3.9900 XPM192 B

AHM5nWRo…724RKRRp

e003dc0df92a52…cdffa6adbcf359

1 in → 2 out0.6428 XPM227 B

APSh2Gn7…h91WQMMU AMWYzRCh…EeeAruqZ

70f6a6fafdd8e4…43e9acf7f27133

1 in → 2 out0.0416 XPM225 B

APJ1nRCZ…REpwqVrG Ae1UJ59y…unMpqUXf

5691e066bfa1d8…066a2ab86c49dc

1 in → 2 out0.0401 XPM226 B

AKRFnvdC…o5XX6WtY AehCVwbF…gQxghmEj

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.

3.275 × 10⁹³(94-digit number)

32755146446434701909…36799544920211544319

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

3.275 × 10⁹³(94-digit number)

32755146446434701909…36799544920211544319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.275 × 10⁹³(94-digit number)

32755146446434701909…36799544920211544321

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

6.551 × 10⁹³(94-digit number)

65510292892869403819…73599089840423088639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.551 × 10⁹³(94-digit number)

65510292892869403819…73599089840423088641

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

1.310 × 10⁹⁴(95-digit number)

13102058578573880763…47198179680846177279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.310 × 10⁹⁴(95-digit number)

13102058578573880763…47198179680846177281

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

2.620 × 10⁹⁴(95-digit number)

26204117157147761527…94396359361692354559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.620 × 10⁹⁴(95-digit number)

26204117157147761527…94396359361692354561

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

5.240 × 10⁹⁴(95-digit number)

52408234314295523055…88792718723384709119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.240 × 10⁹⁴(95-digit number)

52408234314295523055…88792718723384709121

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

Block #857,128

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