Block #336,615

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/31/2013, 2:16:48 AM · Difficulty 10.1414 · 6,473,518 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f8bec4eb0fbab5ccc02e7545f74c7a1c7ea3ea9491e367eedfd6faccbec41819

View on Chainz ↗

Height

#336,615

Difficulty

10.141441

Transactions

Size

1.92 KB

Version

Bits

0a24357f

Nonce

20,793

Timestamp

12/31/2013, 2:16:48 AM

Confirmations

6,473,518

Mined by

⛏️ "aRAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

db187c6aaf7d8945d61fefa9c59ccc6d7f097149ef351d652dfc3681863d5513

Transactions (4)

Coinbase8c13d768febf21…0e4f903cbc4d5e

1 in → 26 out9.7100 XPM947 B

Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AQ8QAT3J…rCFKuVbR Ad9pSzHt…cpJ3y2zz AZPeww38…Qa1u3JLP

dce764c2032713…a65b6c5aad051a

2 in → 7 out19.4800 XPM475 B

AaPaZJvS…ED6BkdmD ASUDdu12…YS6UsfsU AXDEZh15…FbrAPGkC AHnSFGh9…igeoL2xU AeKNrjNj…1NEq95Ta

8ecabf242f8d57…4903878c4a478c

1 in → 2 out8.5870 XPM226 B

AaEQfDed…5MY9m8By AWRThk1H…NVtxeiWc

c2ec4842298d72…769f1fe7921cbb

1 in → 2 out8.5800 XPM226 B

AZT9Bd95…9cSPhH2x AZ8qZ7w8…jtGEbxRH

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.

8.588 × 10⁹³(94-digit number)

85884117402888283343…43990346290054399969

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

8.588 × 10⁹³(94-digit number)

85884117402888283343…43990346290054399969

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.588 × 10⁹³(94-digit number)

85884117402888283343…43990346290054399971

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

1.717 × 10⁹⁴(95-digit number)

17176823480577656668…87980692580108799939

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.717 × 10⁹⁴(95-digit number)

17176823480577656668…87980692580108799941

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

3.435 × 10⁹⁴(95-digit number)

34353646961155313337…75961385160217599879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.435 × 10⁹⁴(95-digit number)

34353646961155313337…75961385160217599881

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

6.870 × 10⁹⁴(95-digit number)

68707293922310626675…51922770320435199759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.870 × 10⁹⁴(95-digit number)

68707293922310626675…51922770320435199761

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

1.374 × 10⁹⁵(96-digit number)

13741458784462125335…03845540640870399519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.374 × 10⁹⁵(96-digit number)

13741458784462125335…03845540640870399521

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 #336,615

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