Block #679,868

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/16/2014, 7:01:06 AM · Difficulty 10.9629 · 6,118,514 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

554db23b9dcce853bc5c940a258571f44b44625887e28605662d7d5978dc7302

View on Chainz ↗

Height

#679,868

Difficulty

10.962933

Transactions

Size

953 B

Version

Bits

0af682c1

Nonce

53,824,841

Timestamp

8/16/2014, 7:01:06 AM

Confirmations

6,118,514

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ac45f7ea5c19ed86d25b2ca4a4fb28332cc56bb1ebbd7f2a41fbcfa48463fc11

Transactions (3)

Coinbase9face100937af3…bceb4e7dac2cc9

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

cbc6d2704d0a77…fa3b4351585e9e

3 in → 2 out22.8495 XPM520 B

APZZjcPT…mEjtCRTo AYeeSCsm…8r7NRrpi

95a484ca8341c8…72e752a745a384

1 in → 2 out7.1948 XPM226 B

AdFaBxm7…71yALtBd AQbXQJ4K…SZFydyis

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.

3.537 × 10⁹⁷(98-digit number)

35373570952820359451…44248854357919033599

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

3.537 × 10⁹⁷(98-digit number)

35373570952820359451…44248854357919033599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.537 × 10⁹⁷(98-digit number)

35373570952820359451…44248854357919033601

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

7.074 × 10⁹⁷(98-digit number)

70747141905640718903…88497708715838067199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.074 × 10⁹⁷(98-digit number)

70747141905640718903…88497708715838067201

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

1.414 × 10⁹⁸(99-digit number)

14149428381128143780…76995417431676134399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.414 × 10⁹⁸(99-digit number)

14149428381128143780…76995417431676134401

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

2.829 × 10⁹⁸(99-digit number)

28298856762256287561…53990834863352268799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.829 × 10⁹⁸(99-digit number)

28298856762256287561…53990834863352268801

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

5.659 × 10⁹⁸(99-digit number)

56597713524512575122…07981669726704537599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.659 × 10⁹⁸(99-digit number)

56597713524512575122…07981669726704537601

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

1.131 × 10⁹⁹(100-digit number)

11319542704902515024…15963339453409075199

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