Block #841,126

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/5/2014, 4:03:32 PM · Difficulty 10.9741 · 6,002,545 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

91bc80dd7aeb29f709f886ebcaf079af310b451c6cd73ae1ad04de57fcc4501b

View on Chainz ↗

Height

#841,126

Difficulty

10.974076

Transactions

Size

886 B

Version

Bits

0af95d0a

Nonce

38,405,851

Timestamp

12/5/2014, 4:03:32 PM

Confirmations

6,002,545

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

a5b8388ce2b2337a8738cdaaa1c22798121ab35cb0ffffe2f5b10551ba9baa93

Transactions (4)

Coinbasea3042b9b3ee1d0…2e851d41236900

1 in → 1 out8.3350 XPM116 B

ANSXnLY2…Sd25TjkD

ca60580dff6c0f…c4b0ecf5db10b9

1 in → 2 out0.0946 XPM226 B

Adkr4aZC…1u4PF3eX AKM48Xu2…r9SivCap

a6379a3b481fc3…245c58b15b7efb

1 in → 2 out0.0533 XPM226 B

ARBnJiq4…jKRW3d6Q AHGR3WYC…szWbUTJN

f4ac05c6aa75f3…36aa66c2e98683

1 in → 2 out0.0408 XPM226 B

AXnZzX9s…N3Hsaqxn Ad4QsneG…iCiFRfk2

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.

7.947 × 10⁹⁸(99-digit number)

79474590936255957959…25350146364919295999

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

7.947 × 10⁹⁸(99-digit number)

79474590936255957959…25350146364919295999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.947 × 10⁹⁸(99-digit number)

79474590936255957959…25350146364919296001

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

1.589 × 10⁹⁹(100-digit number)

15894918187251191591…50700292729838591999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.589 × 10⁹⁹(100-digit number)

15894918187251191591…50700292729838592001

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

3.178 × 10⁹⁹(100-digit number)

31789836374502383183…01400585459677183999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.178 × 10⁹⁹(100-digit number)

31789836374502383183…01400585459677184001

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

6.357 × 10⁹⁹(100-digit number)

63579672749004766367…02801170919354367999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.357 × 10⁹⁹(100-digit number)

63579672749004766367…02801170919354368001

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

1.271 × 10¹⁰⁰(101-digit number)

12715934549800953273…05602341838708735999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.271 × 10¹⁰⁰(101-digit number)

12715934549800953273…05602341838708736001

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

2.543 × 10¹⁰⁰(101-digit number)

25431869099601906546…11204683677417471999

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 #841,126

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