Block #947,930

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/22/2015, 8:30:42 PM · Difficulty 10.8990 · 5,867,212 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3e025c56dd8c1bdd3a927be7c3296f50547217caa3ee1805df2ef44a51484601

View on Chainz ↗

Height

#947,930

Difficulty

10.899003

Transactions

Size

1.73 KB

Version

Bits

0ae62517

Nonce

614,935,535

Timestamp

2/22/2015, 8:30:42 PM

Confirmations

5,867,212

Mined by

⛏️ P2SHAe6f4mphWstxJoBPNy21LABJUnpmZiLHNH

Merkle Root

018b63ba97cac4096c2428ad8f3bc98142cc0f0b375b1ccf94b4db62ce147e0b

Transactions (4)

Coinbaseb2856f9554b564…9e8f97e8b965be

1 in → 1 out8.4300 XPM109 B

Ae6f4mph…pmZiLHNH

e8e1fe56686d18…c6d1da8b26f2cd

6 in → 2 out50.4700 XPM968 B

AJrRCXQ6…JfrPVgfE AGPmAj3Y…fzst5xwP

cd4e6af037c6b5…530ba1d65ff941

2 in → 2 out14.8670 XPM375 B

AHxSJ5MR…cLPMMk3Q AdUwqsJC…kyCDagPM

8cc26d01b74976…5088ee8cd63dff

1 in → 2 out6.6208 XPM226 B

AQFpxGYM…jgECkwsL ANia7wgK…VR264iFL

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.

6.759 × 10⁹²(93-digit number)

67594974893735444563…04963475036964279679

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

6.759 × 10⁹²(93-digit number)

67594974893735444563…04963475036964279679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.759 × 10⁹²(93-digit number)

67594974893735444563…04963475036964279681

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

1.351 × 10⁹³(94-digit number)

13518994978747088912…09926950073928559359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.351 × 10⁹³(94-digit number)

13518994978747088912…09926950073928559361

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

2.703 × 10⁹³(94-digit number)

27037989957494177825…19853900147857118719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.703 × 10⁹³(94-digit number)

27037989957494177825…19853900147857118721

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

5.407 × 10⁹³(94-digit number)

54075979914988355650…39707800295714237439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.407 × 10⁹³(94-digit number)

54075979914988355650…39707800295714237441

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

1.081 × 10⁹⁴(95-digit number)

10815195982997671130…79415600591428474879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.081 × 10⁹⁴(95-digit number)

10815195982997671130…79415600591428474881

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 #947,930

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