Block #294,648

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/4/2013, 11:55:45 PM · Difficulty 9.9911 · 6,512,082 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

496d016f38ec19866368940e9669823de11cd110568ce1a6ec9794c3ba92a96b

View on Chainz ↗

Height

#294,648

Difficulty

9.991113

Transactions

Size

2.78 KB

Version

Bits

09fdb993

Nonce

16,706

Timestamp

12/4/2013, 11:55:45 PM

Confirmations

6,512,082

Mined by

⛏️ ~aRAd9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

96b1084bbdf4e7d798e4b698de5eb2683c5ac26d574d0cc4f74b015f5311ab6a

Transactions (4)

Coinbase7cf67287471372…ec4435868faea0

1 in → 30 out9.9800 XPM1.06 KB

Ad9pSzHt…cpJ3y2zz ARcqMJhp…RVLToQ6S AHuJ9wYh…BGmgHrKZ AQwRN8bE…V8PsTcY9 AZ2pPuKg…95SN2Yr7

b1d7a9d5ef6634…afd607b75f822a

10 in → 2 out101.0500 XPM1.19 KB

AYzsMZt3…DmU2Unhv AG7MairC…vupDLdC7

b2e8d73b2d8ef9…d5d09d3df777dc

1 in → 2 out6.8053 XPM227 B

AYYbfTF2…Mz7DLHsV AKBityws…1GAbJmiE

ed9e924a733a63…e5a56432d9aed8

1 in → 2 out5.6498 XPM225 B

AXFrbPHq…WJ7Htzc7 AUZkT4EK…YJeWAx7s

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.

4.494 × 10⁹²(93-digit number)

44943402886137039347…78405052887166749059

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

4.494 × 10⁹²(93-digit number)

44943402886137039347…78405052887166749059

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.494 × 10⁹²(93-digit number)

44943402886137039347…78405052887166749061

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

8.988 × 10⁹²(93-digit number)

89886805772274078695…56810105774333498119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.988 × 10⁹²(93-digit number)

89886805772274078695…56810105774333498121

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

1.797 × 10⁹³(94-digit number)

17977361154454815739…13620211548666996239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.797 × 10⁹³(94-digit number)

17977361154454815739…13620211548666996241

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

3.595 × 10⁹³(94-digit number)

35954722308909631478…27240423097333992479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.595 × 10⁹³(94-digit number)

35954722308909631478…27240423097333992481

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

7.190 × 10⁹³(94-digit number)

71909444617819262956…54480846194667984959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.190 × 10⁹³(94-digit number)

71909444617819262956…54480846194667984961

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 #294,648

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