Block #330,751

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/26/2013, 9:50:17 PM · Difficulty 10.1658 · 6,461,989 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b50ced724eabce93684f33a427d2eff0c5dbfd665a82ff206efa8be73e95ed13

View on Chainz ↗

Height

#330,751

Difficulty

10.165791

Transactions

Size

1.22 KB

Version

Bits

0a2a7148

Nonce

97,383

Timestamp

12/26/2013, 9:50:17 PM

Confirmations

6,461,989

Merkle Root

ec74bbe82a514a48b5223dcae9c06e8fdef2a313319693b1c7e180c38736dc9e

Transactions (5)

Coinbasefaadcef40e47cd…b49cbd4eb558f3

1 in → 1 out9.7000 XPM109 B

AP5EB2Lp…PJzTgh84

fd0daacead9fc7…6d9d46a38f6c25

1 in → 2 out7.5373 XPM226 B

ALGoNmyS…oRwg8sE1 Abyyn7db…qUUWKdct

7bd58bb9b77f9b…06df3c878f2898

1 in → 2 out5.4733 XPM226 B

AYwfaFgG…Dcadp6aq ANECpbxd…XLvANQZs

4a665cf2b0fdd2…7f148a179f42f6

1 in → 2 out5.3137 XPM227 B

Ad6d97Lu…68YtqjRu AJHMeUzo…o5EQTvMg

21ffbc73046b7a…945e60f7b252b7

2 in → 2 out1.1202 XPM373 B

AMBaesuK…6AGZoQG4 AcKNLqTp…CnobUfzD

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.

2.255 × 10¹⁰¹(102-digit number)

22552315253104200373…63908540966993191999

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

2.255 × 10¹⁰¹(102-digit number)

22552315253104200373…63908540966993191999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.255 × 10¹⁰¹(102-digit number)

22552315253104200373…63908540966993192001

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

4.510 × 10¹⁰¹(102-digit number)

45104630506208400746…27817081933986383999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.510 × 10¹⁰¹(102-digit number)

45104630506208400746…27817081933986384001

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

9.020 × 10¹⁰¹(102-digit number)

90209261012416801492…55634163867972767999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.020 × 10¹⁰¹(102-digit number)

90209261012416801492…55634163867972768001

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

1.804 × 10¹⁰²(103-digit number)

18041852202483360298…11268327735945535999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.804 × 10¹⁰²(103-digit number)

18041852202483360298…11268327735945536001

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

3.608 × 10¹⁰²(103-digit number)

36083704404966720597…22536655471891071999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.608 × 10¹⁰²(103-digit number)

36083704404966720597…22536655471891072001

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