Block #278,831

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 3:25:14 AM · Difficulty 9.9700 · 6,526,177 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

67637165defcb5c776fb5b1cc8617b830cbe866a569c2bd67851d565c2fc850d

View on Chainz ↗

Height

#278,831

Difficulty

9.970012

Transactions

Size

1.39 KB

Version

Bits

09f852bc

Nonce

26,556

Timestamp

11/28/2013, 3:25:14 AM

Confirmations

6,526,177

Mined by

⛏️ AAYZUGpXaKqJ144HRZuhFHsJcejW7UKsvcT

Merkle Root

77198c2d6ff9391fb64a0178fad54e665e7c6377c62c6410252987dc50a4beaf

Transactions (4)

Coinbasea7965d85c3f5a6…3ae5397bfe7565

1 in → 1 out10.0800 XPM109 B

AYZUGpXa…W7UKsvcT

dcfaf70bf4c652…e8e9f54dff5cff

4 in → 9 out40.3900 XPM771 B

ARNr2Qfw…M9N1vs43 ALanGMzb…mpKXHzz4 AeKNrjNj…1NEq95Ta AYiuPkxV…9nUvdUg1 ASnV7gd8…ErTxWewi

0e3f78c01b642b…56954e2b66b957

1 in → 2 out6.9974 XPM227 B

AdpotGpu…gLw1BphZ ARQif6E9…2dukv8CL

37be97a3203bd9…e4d63f0afcaf37

1 in → 2 out1.0962 XPM227 B

AcVtD4US…qhxBcicn AR2XnKEr…eUyCwEd5

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.

3.362 × 10⁹²(93-digit number)

33623311542062069000…65169515587860284319

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

3.362 × 10⁹²(93-digit number)

33623311542062069000…65169515587860284319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.362 × 10⁹²(93-digit number)

33623311542062069000…65169515587860284321

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

6.724 × 10⁹²(93-digit number)

67246623084124138001…30339031175720568639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.724 × 10⁹²(93-digit number)

67246623084124138001…30339031175720568641

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

1.344 × 10⁹³(94-digit number)

13449324616824827600…60678062351441137279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.344 × 10⁹³(94-digit number)

13449324616824827600…60678062351441137281

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

2.689 × 10⁹³(94-digit number)

26898649233649655200…21356124702882274559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.689 × 10⁹³(94-digit number)

26898649233649655200…21356124702882274561

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

5.379 × 10⁹³(94-digit number)

53797298467299310401…42712249405764549119

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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