Block #285,030

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 8:37:09 AM · Difficulty 9.9836 · 6,524,945 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d2638852fe41d9d33dda85de90b28ef1025db4f2c8768e166f661807c9d2b39b

View on Chainz ↗

Height

#285,030

Difficulty

9.983635

Transactions

Size

1.07 KB

Version

Bits

09fbcf82

Nonce

65,985

Timestamp

11/30/2013, 8:37:09 AM

Confirmations

6,524,945

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

e53b1254924e0b2ecb693b386aff17e6583c1f41b44f417bac60c99a148f5091

Transactions (3)

Coinbase2c72306392935f…db2f9914972922

1 in → 1 out10.0400 XPM110 B

AeKNrjNj…1NEq95Ta

060cba0ca1d4b2…c7c7a27ce2f1ee

1 in → 2 out19.7900 XPM226 B

AHqDAkE7…cosGPsfW AJX1LfUv…UGofRh5j

0f9f5e37c034e8…33c08213c33d9f

4 in → 2 out38.2931 XPM670 B

ANASbiVb…WPXRuF43 AY43ujT1…HsxJFyXL

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.

8.925 × 10⁹¹(92-digit number)

89253919690078404092…38406403682002117199

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

8.925 × 10⁹¹(92-digit number)

89253919690078404092…38406403682002117199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.925 × 10⁹¹(92-digit number)

89253919690078404092…38406403682002117201

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

1.785 × 10⁹²(93-digit number)

17850783938015680818…76812807364004234399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.785 × 10⁹²(93-digit number)

17850783938015680818…76812807364004234401

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

3.570 × 10⁹²(93-digit number)

35701567876031361637…53625614728008468799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.570 × 10⁹²(93-digit number)

35701567876031361637…53625614728008468801

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

7.140 × 10⁹²(93-digit number)

71403135752062723274…07251229456016937599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.140 × 10⁹²(93-digit number)

71403135752062723274…07251229456016937601

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

1.428 × 10⁹³(94-digit number)

14280627150412544654…14502458912033875199

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

Block #285,030

Cookie Preferences