Block #315,083

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/16/2013, 8:08:56 AM · Difficulty 10.0849 · 6,491,732 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

467d2d8850bf1d039b58ed693da9b9b08cf2bdffd1c66ce3be7e1f27842538fe

View on Chainz ↗

Height

#315,083

Difficulty

10.084948

Transactions

Size

3.14 KB

Version

Bits

0a15bf27

Nonce

173,183

Timestamp

12/16/2013, 8:08:56 AM

Confirmations

6,491,732

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

4111ca9fcee14af56392ef85057be7a5147b77484e7efe303e84fe589256cc67

Transactions (4)

Coinbase93b3c2aefcd25a…ef8af322b5b923

1 in → 1 out9.8753 XPM110 B

AeKNrjNj…1NEq95Ta

108558f62d1229…4caebe53408e5a

16 in → 1 out5.3500 XPM2.36 KB

AGJWTJSh…vFzqi4AE

9d029a0d9fd38d…e2c9e337537af6

1 in → 2 out8.9658 XPM225 B

AemQB9dc…KANt1FMV AGGBHjPT…LTXztLV6

400e62fe87a767…f050c47e8faead

2 in → 2 out1.1648 XPM374 B

AYtNdHZa…5vztQmDq ASb1CwwX…zYxGLhT7

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.

3.000 × 10⁹⁸(99-digit number)

30007116560652528160…71625382958386854919

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

3.000 × 10⁹⁸(99-digit number)

30007116560652528160…71625382958386854919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.000 × 10⁹⁸(99-digit number)

30007116560652528160…71625382958386854921

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

6.001 × 10⁹⁸(99-digit number)

60014233121305056320…43250765916773709839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.001 × 10⁹⁸(99-digit number)

60014233121305056320…43250765916773709841

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

1.200 × 10⁹⁹(100-digit number)

12002846624261011264…86501531833547419679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.200 × 10⁹⁹(100-digit number)

12002846624261011264…86501531833547419681

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

2.400 × 10⁹⁹(100-digit number)

24005693248522022528…73003063667094839359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.400 × 10⁹⁹(100-digit number)

24005693248522022528…73003063667094839361

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

4.801 × 10⁹⁹(100-digit number)

48011386497044045056…46006127334189678719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.801 × 10⁹⁹(100-digit number)

48011386497044045056…46006127334189678721

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 #315,083

Cookie Preferences