Block #682,315

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/18/2014, 4:35:49 AM · Difficulty 10.9608 · 6,122,728 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

caa6b24a7a3b01b406cd890a8f744a6fb24b0564cd85bf0c8f9e38f405b5c8b8

View on Chainz ↗

Height

#682,315

Difficulty

10.960837

Transactions

Size

914 B

Version

Bits

0af5f969

Nonce

199,825,718

Timestamp

8/18/2014, 4:35:49 AM

Confirmations

6,122,728

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b56de9b1f210b5f0a1e3d51e2c478315bb1c3abccc359af17d35df04f00b8601

Transactions (2)

Coinbase9eff8292ac38e0…c88fa1892fea91

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

09ffd5986d374b…eb716dbe065eb4

4 in → 3 out6.1035 XPM706 B

AcNovFbg…sJ1oLH5E ALeH3dPN…zVgWRzZU AeKNrjNj…1NEq95Ta

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.

5.633 × 10⁹⁹(100-digit number)

56333335828166837036…67981208953984450559

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

5.633 × 10⁹⁹(100-digit number)

56333335828166837036…67981208953984450559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.633 × 10⁹⁹(100-digit number)

56333335828166837036…67981208953984450561

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

1.126 × 10¹⁰⁰(101-digit number)

11266667165633367407…35962417907968901119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.126 × 10¹⁰⁰(101-digit number)

11266667165633367407…35962417907968901121

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

2.253 × 10¹⁰⁰(101-digit number)

22533334331266734814…71924835815937802239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.253 × 10¹⁰⁰(101-digit number)

22533334331266734814…71924835815937802241

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

4.506 × 10¹⁰⁰(101-digit number)

45066668662533469629…43849671631875604479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.506 × 10¹⁰⁰(101-digit number)

45066668662533469629…43849671631875604481

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

9.013 × 10¹⁰⁰(101-digit number)

90133337325066939258…87699343263751208959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.013 × 10¹⁰⁰(101-digit number)

90133337325066939258…87699343263751208961

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