Block #848,982

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/11/2014, 12:13:00 PM · Difficulty 10.9713 · 5,987,871 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fb71fec57e6d7bb43dda8f1a6bfa5090acdb3fec7274f66b437d0e111572fca4

View on Chainz ↗

Height

#848,982

Difficulty

10.971325

Transactions

Size

881 B

Version

Bits

0af8a8be

Nonce

1,281,024,663

Timestamp

12/11/2014, 12:13:00 PM

Confirmations

5,987,871

Mined by

⛏️ P2SHAXwM1mLqr6gxR4tYHN3LnxVnkB6NVTcaoS

Merkle Root

a995f961444b204a1880be5a63b25514a2ca5313293a927cc4ede1ba0a5d8685

Transactions (4)

Coinbasee21bc2b5fe5069…2ddc1d4b2ff142

1 in → 1 out8.3350 XPM110 B

AXwM1mLq…6NVTcaoS

8dcc12d8a421b5…c4b2f609958a1a

1 in → 2 out0.1169 XPM227 B

AXsnsgJZ…KvXwXgyy AMKVBys2…RwgTfMQg

ccf2b139f19e49…7b4d572f5d1e6a

1 in → 2 out0.0379 XPM227 B

AJyhUr8G…swDgwbme AHoszKw8…Q8XaWx6o

cc8d36d43fca6a…b536b172d7d671

1 in → 2 out0.0377 XPM227 B

AXa9fDAs…dZLZCJ9k AXUvaafh…RzAy1cjC

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.

4.741 × 10⁹⁴(95-digit number)

47411325326731236343…55681028508575852799

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

4.741 × 10⁹⁴(95-digit number)

47411325326731236343…55681028508575852799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.741 × 10⁹⁴(95-digit number)

47411325326731236343…55681028508575852801

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

9.482 × 10⁹⁴(95-digit number)

94822650653462472686…11362057017151705599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.482 × 10⁹⁴(95-digit number)

94822650653462472686…11362057017151705601

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

1.896 × 10⁹⁵(96-digit number)

18964530130692494537…22724114034303411199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.896 × 10⁹⁵(96-digit number)

18964530130692494537…22724114034303411201

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

3.792 × 10⁹⁵(96-digit number)

37929060261384989074…45448228068606822399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.792 × 10⁹⁵(96-digit number)

37929060261384989074…45448228068606822401

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

7.585 × 10⁹⁵(96-digit number)

75858120522769978148…90896456137213644799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.585 × 10⁹⁵(96-digit number)

75858120522769978148…90896456137213644801

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

1.517 × 10⁹⁶(97-digit number)

15171624104553995629…81792912274427289599

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

Block #848,982

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