Block #841,382

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/5/2014, 8:29:16 PM · Difficulty 10.9740 · 5,972,742 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2f3905de766e76813badc50394b4cf3236b7b5c03855a861e76d2c76d2b36381

View on Chainz ↗

Height

#841,382

Difficulty

10.974045

Transactions

Size

807 B

Version

Bits

0af95aff

Nonce

1,514,183,655

Timestamp

12/5/2014, 8:29:16 PM

Confirmations

5,972,742

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

3a2ab098afc44b9cded226531f3c7d76b598cbb1d28db98a4eb866632a55a01f

Transactions (3)

Coinbase2f04f8d9b5e391…99401ec3458b2f

1 in → 1 out8.3150 XPM116 B

ANSXnLY2…Sd25TjkD

b331956475e067…3fcda41bec67ba

2 in → 2 out14.5061 XPM374 B

AWAbb2pL…4Wmht5QK AUv61ksA…jTKMrrzs

7de7a1dacb8eb7…eee329f9aa4444

1 in → 2 out0.0661 XPM226 B

ARe2XaKS…WfbSvwoA AStp2xBF…BNdYLHbm

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.

1.565 × 10⁹⁸(99-digit number)

15657657167110689222…89493448213097727999

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

1.565 × 10⁹⁸(99-digit number)

15657657167110689222…89493448213097727999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.565 × 10⁹⁸(99-digit number)

15657657167110689222…89493448213097728001

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

3.131 × 10⁹⁸(99-digit number)

31315314334221378444…78986896426195455999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.131 × 10⁹⁸(99-digit number)

31315314334221378444…78986896426195456001

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

6.263 × 10⁹⁸(99-digit number)

62630628668442756889…57973792852390911999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.263 × 10⁹⁸(99-digit number)

62630628668442756889…57973792852390912001

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

1.252 × 10⁹⁹(100-digit number)

12526125733688551377…15947585704781823999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.252 × 10⁹⁹(100-digit number)

12526125733688551377…15947585704781824001

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

2.505 × 10⁹⁹(100-digit number)

25052251467377102755…31895171409563647999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.505 × 10⁹⁹(100-digit number)

25052251467377102755…31895171409563648001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

5.010 × 10⁹⁹(100-digit number)

50104502934754205511…63790342819127295999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #841,382

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