Block #332,480

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/28/2013, 2:14:41 AM · Difficulty 10.1706 · 6,470,890 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6f19a03342d021fe0751ca44fa8f7d7c8d503c9993d49fbebeb7e861c8fde2df

View on Chainz ↗

Height

#332,480

Difficulty

10.170603

Transactions

Size

1.51 KB

Version

Bits

0a2baca7

Nonce

83,592

Timestamp

12/28/2013, 2:14:41 AM

Confirmations

6,470,890

Mined by

⛏️ P2SHAc9EH9A7VqG22r9gM5rdnApiJuptU3Cwvc

Merkle Root

079e1652520018be918161f6c923cf4d628baf2e965dc3030bc1ea370bf4b4a0

Transactions (5)

Coinbaseba229e849df57b…7a716a78252e5d

1 in → 1 out9.6900 XPM109 B

Ac9EH9A7…ptU3Cwvc

da955b56f6ba11…a6b1e99caf72d2

4 in → 2 out10.0275 XPM670 B

ASuoUi24…FwBoFbxd AH5BTxmB…kt9NdZoT

37884e7a6b596d…42b5efb57422ab

1 in → 2 out8.5890 XPM226 B

ASTku6PZ…vgHqTkGk Ac24WwPt…BSeTbxUj

44843212cc7ee8…dd7739104cf337

1 in → 2 out7.5779 XPM227 B

AVbZXJ3t…rUfwNaLf AQhJqhrV…3NcAJdQq

1dda65ba8e9d02…bc2778f274c59a

1 in → 2 out7.5775 XPM227 B

AHhoZ2RK…7MyUc4Xr AY9AtywP…quXiBg7X

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.

2.502 × 10⁹⁸(99-digit number)

25020051268633309748…30958480799056887479

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

2.502 × 10⁹⁸(99-digit number)

25020051268633309748…30958480799056887479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.502 × 10⁹⁸(99-digit number)

25020051268633309748…30958480799056887481

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

5.004 × 10⁹⁸(99-digit number)

50040102537266619497…61916961598113774959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.004 × 10⁹⁸(99-digit number)

50040102537266619497…61916961598113774961

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

1.000 × 10⁹⁹(100-digit number)

10008020507453323899…23833923196227549919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.000 × 10⁹⁹(100-digit number)

10008020507453323899…23833923196227549921

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

2.001 × 10⁹⁹(100-digit number)

20016041014906647798…47667846392455099839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.001 × 10⁹⁹(100-digit number)

20016041014906647798…47667846392455099841

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

4.003 × 10⁹⁹(100-digit number)

40032082029813295597…95335692784910199679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.003 × 10⁹⁹(100-digit number)

40032082029813295597…95335692784910199681

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