Block #308,379

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/13/2013, 2:08:39 AM · Difficulty 9.9945 · 6,501,134 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3dbe0c9c46f5c7cd3f6445f489412682de466698d55cd24a547a909230816599

View on Chainz ↗

Height

#308,379

Difficulty

9.994471

Transactions

Size

107.01 KB

Version

Bits

09fe95a9

Nonce

39,373

Timestamp

12/13/2013, 2:08:39 AM

Confirmations

6,501,134

Mined by

⛏️ P2SHAGoigCUHTjV4u6Xq95UoYZGNhX78feNnQR

Merkle Root

e767d262e6c00b731b88a4144ee0b3d98351fd707ef67cea4dac726e96df8acf

Transactions (5)

Coinbase68f2da41b4dcba…e8d85a037c617a

1 in → 1 out11.1227 XPM109 B

AGoigCUH…78feNnQR

a552103424c7e4…b2e85bba317032

6 in → 1 out104.7200 XPM726 B

AUc9f75K…XkgyC4YK

95512661ca8b28…d9a9e4ea88454a

534 in → 2 out200.0100 XPM77.24 KB

AYoLP1Qt…WfK9FPgP AMNiThRd…VoxeMbvm

91e4ba9166fca9…dc92b2580de840

20 in → 1 out6.1000 XPM2.94 KB

AWZoaFiX…YzJJ81GU

8d4392aae91b9d…2c279ed3f64047

179 in → 2 out63.1848 XPM25.93 KB

ATxhLGpf…Pw6jz86y ANhReCJL…41yYT6kX

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.

4.440 × 10⁹⁴(95-digit number)

44409184106017760330…51433017718988654399

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

4.440 × 10⁹⁴(95-digit number)

44409184106017760330…51433017718988654399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.440 × 10⁹⁴(95-digit number)

44409184106017760330…51433017718988654401

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

8.881 × 10⁹⁴(95-digit number)

88818368212035520661…02866035437977308799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.881 × 10⁹⁴(95-digit number)

88818368212035520661…02866035437977308801

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

1.776 × 10⁹⁵(96-digit number)

17763673642407104132…05732070875954617599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.776 × 10⁹⁵(96-digit number)

17763673642407104132…05732070875954617601

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

3.552 × 10⁹⁵(96-digit number)

35527347284814208264…11464141751909235199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.552 × 10⁹⁵(96-digit number)

35527347284814208264…11464141751909235201

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

7.105 × 10⁹⁵(96-digit number)

71054694569628416528…22928283503818470399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.105 × 10⁹⁵(96-digit number)

71054694569628416528…22928283503818470401

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 #308,379

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