Block #405,577

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/15/2014, 4:06:37 PM · Difficulty 10.4314 · 6,390,710 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

90bf50fa264b1db7ae30d6dee1a93850bec6ea5eadcf4e33df20925574f8f8d6

View on Chainz ↗

Height

#405,577

Difficulty

10.431412

Transactions

Size

2.22 KB

Version

Bits

0a6e7107

Nonce

5,146

Timestamp

2/15/2014, 4:06:37 PM

Confirmations

6,390,710

Mined by

⛏️ I0eAMW1p9oTkBzM1hi3okaKfJzfWi2TzdaZxH

Merkle Root

ddb1486960852069563e4b5005cf8b74bdb63577869bf9395075c4ca07aa60bb

Transactions (5)

Coinbase7d9af343645eec…008470c007ab67

1 in → 23 out9.2200 XPM845 B

AMW1p9oT…2TzdaZxH AcgDwGo8…BBFwbjVo AW2fas42…gGAHYdHj AZr7Ptuw…CM4Yw5jq AXCBfU18…vZFjKTCm

a84ccc99af1727…745506dc2260dd

3 in → 9 out27.6000 XPM659 B

AZEVTKtj…amufabqp AeKNrjNj…1NEq95Ta AMieFDLv…pGBrcTXb AQYQT37a…woJiw19q AdTtZYv4…mEzssnpx

1a8d4a2fc628ae…6395165f40d45e

1 in → 2 out5.0869 XPM227 B

AGiDuDeS…V1EbLtmr AGxMeQpn…PtE4vAxN

94294f9780ebb7…d5ad27d0ee6e8b

1 in → 2 out2.5505 XPM226 B

AZ3jhwb7…GQpb6GPh AXe2aBLP…CXgpWDWt

8b504e58a5f1ab…fd190eb6dc35f1

1 in → 2 out1.1238 XPM227 B

AULjZ68a…PK7TaBdd AXnL68UR…jsxeGUhN

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.

5.123 × 10⁹⁶(97-digit number)

51235757007692379034…64672305126592891269

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

5.123 × 10⁹⁶(97-digit number)

51235757007692379034…64672305126592891269

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.123 × 10⁹⁶(97-digit number)

51235757007692379034…64672305126592891271

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

1.024 × 10⁹⁷(98-digit number)

10247151401538475806…29344610253185782539

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.024 × 10⁹⁷(98-digit number)

10247151401538475806…29344610253185782541

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

2.049 × 10⁹⁷(98-digit number)

20494302803076951613…58689220506371565079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.049 × 10⁹⁷(98-digit number)

20494302803076951613…58689220506371565081

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

4.098 × 10⁹⁷(98-digit number)

40988605606153903227…17378441012743130159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.098 × 10⁹⁷(98-digit number)

40988605606153903227…17378441012743130161

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

8.197 × 10⁹⁷(98-digit number)

81977211212307806454…34756882025486260319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.197 × 10⁹⁷(98-digit number)

81977211212307806454…34756882025486260321

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