Block #284,700

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 5:25:52 AM · Difficulty 9.9832 · 6,524,823 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b519895b5f8699f444142982389de1e3af228416ee4ceca918774b4d53731961

View on Chainz ↗

Height

#284,700

Difficulty

9.983168

Transactions

Size

2.31 KB

Version

Bits

09fbb0e6

Nonce

24,139

Timestamp

11/30/2013, 5:25:52 AM

Confirmations

6,524,823

Mined by

⛏️ P2SHAcyKvNQCjLo5YWUNFhZRfSn172CkQkgxQV

Merkle Root

f915ab1b0e75c305a408cccca664389296e04db5d0932c25356f11717f19e9d3

Transactions (5)

Coinbase42574cfae53a9a…ddf407a07a094c

1 in → 1 out10.0700 XPM109 B

AcyKvNQC…CkQkgxQV

5a98e41cd4b17d…ef074397523459

7 in → 20 out70.3800 XPM1.45 KB

AeKNrjNj…1NEq95Ta AJ7bDQSz…fGAfKA56 APYq627z…f4sQNhSZ ASc4k2fS…ngdwoi5i AFsMW6dF…Z3wb5bBq

68f29e9bf84236…4d3d73d27a649d

1 in → 2 out6.5519 XPM227 B

AdiJnPZ2…8NEy6P8S ASJkAEPR…gi4CDeTY

1f6edb5563ca76…9044603fb52c5d

1 in → 2 out4.9690 XPM226 B

ANPmZjPW…3DkV45i8 ARskhKeb…UgDvvX9P

56809844259ede…b30daa5e748753

1 in → 2 out1.7673 XPM227 B

ASrunyiE…d6Edq2bT ANhyi1rD…QSBCPUr3

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.

1.351 × 10⁹⁴(95-digit number)

13519369826533628266…58171196016233422239

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

1.351 × 10⁹⁴(95-digit number)

13519369826533628266…58171196016233422239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.351 × 10⁹⁴(95-digit number)

13519369826533628266…58171196016233422241

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

2.703 × 10⁹⁴(95-digit number)

27038739653067256532…16342392032466844479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.703 × 10⁹⁴(95-digit number)

27038739653067256532…16342392032466844481

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

5.407 × 10⁹⁴(95-digit number)

54077479306134513065…32684784064933688959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.407 × 10⁹⁴(95-digit number)

54077479306134513065…32684784064933688961

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

1.081 × 10⁹⁵(96-digit number)

10815495861226902613…65369568129867377919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.081 × 10⁹⁵(96-digit number)

10815495861226902613…65369568129867377921

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

2.163 × 10⁹⁵(96-digit number)

21630991722453805226…30739136259734755839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.163 × 10⁹⁵(96-digit number)

21630991722453805226…30739136259734755841

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

Block #284,700

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