Block #848,488

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/11/2014, 3:09:29 AM · Difficulty 10.9716 · 5,994,724 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f0587ab65bd415ca7ad3b1936caa7ce2e7f47cb451f711d9d57e6d9faba61ff7

View on Chainz ↗

Height

#848,488

Difficulty

10.971584

Transactions

Size

1.18 KB

Version

Bits

0af8b9c0

Nonce

1,894,883,621

Timestamp

12/11/2014, 3:09:29 AM

Confirmations

5,994,724

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

3d98b7923f33b864e1be0563dc33208823f7177276fae6071b91d07e28177b83

Transactions (4)

Coinbasec04491db79fe4a…172787e7161650

1 in → 1 out8.3426 XPM116 B

ANSXnLY2…Sd25TjkD

fd28c5e3381264…b594f9bfec7f5a

1 in → 3 out0.2247 XPM260 B

ANzcbwMX…BpjTfjGZ AUTSwDpv…98nKM5Uu ASb6Hrvk…J9wSSRpH

c2df5f6b8cddf2…fdb138fa172340

1 in → 3 out0.7199 XPM260 B

AaiCJPz6…uePQ6B8z AMSPkEdJ…sm5Vx57e ATdAha89…u7qqJWwb

6fa18324f5e767…d6d22c350b742b

3 in → 1 out0.0117 XPM486 B

AUoBkFN5…Du9E3UdA

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.

1.894 × 10⁹⁵(96-digit number)

18948029812558412068…60825800252910257719

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

1.894 × 10⁹⁵(96-digit number)

18948029812558412068…60825800252910257719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.894 × 10⁹⁵(96-digit number)

18948029812558412068…60825800252910257721

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

3.789 × 10⁹⁵(96-digit number)

37896059625116824137…21651600505820515439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.789 × 10⁹⁵(96-digit number)

37896059625116824137…21651600505820515441

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

7.579 × 10⁹⁵(96-digit number)

75792119250233648274…43303201011641030879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.579 × 10⁹⁵(96-digit number)

75792119250233648274…43303201011641030881

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

1.515 × 10⁹⁶(97-digit number)

15158423850046729654…86606402023282061759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.515 × 10⁹⁶(97-digit number)

15158423850046729654…86606402023282061761

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

3.031 × 10⁹⁶(97-digit number)

30316847700093459309…73212804046564123519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.031 × 10⁹⁶(97-digit number)

30316847700093459309…73212804046564123521

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

6.063 × 10⁹⁶(97-digit number)

60633695400186918619…46425608093128247039

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 #848,488

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