Block #665,372

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/6/2014, 11:35:15 AM · Difficulty 10.9596 · 6,145,081 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2b4822f6342f8e72bb3830ccc0e6df714c74032d781a249bde4d2b0af829079e

View on Chainz ↗

Height

#665,372

Difficulty

10.959589

Transactions

Size

1.26 KB

Version

Bits

0af5a7a6

Nonce

232,986,194

Timestamp

8/6/2014, 11:35:15 AM

Confirmations

6,145,081

Mined by

⛏️ P2SHAULY2pjcxaZL8LG72BvVyaaH2AephkB2qi

Merkle Root

2d49206d965440ee877227e8a30a654ea564728d20419c14df9347e0e465b39e

Transactions (5)

Coinbase440d07805c290c…6d672124535772

1 in → 1 out8.3500 XPM109 B

AULY2pjc…ephkB2qi

7a54e63905eb22…3de9de7e086cde

1 in → 3 out6.1868 XPM261 B

AeKNrjNj…1NEq95Ta AHrFNmf8…hpqU2WtU AH1wEe2R…srAfPtHd

ac530cbbfc0623…2117364c217b8b

1 in → 2 out6.1026 XPM227 B

AKjFveug…bMhAs7sf AU4sFDHf…wbpXP1pK

20238ce093c70b…f2bbfc331b1456

1 in → 2 out5.5751 XPM226 B

AXme6eTz…PLdysKBL AYU8xKop…CrrBWkH7

da8860ed6aa459…a45b7f97bb02cf

2 in → 2 out8.1922 XPM373 B

AdmPkeDX…skr8zPN5 AcKerPva…qeeuPChG

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.

3.174 × 10⁹⁴(95-digit number)

31744187672710985004…09123378099030873599

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

3.174 × 10⁹⁴(95-digit number)

31744187672710985004…09123378099030873599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.174 × 10⁹⁴(95-digit number)

31744187672710985004…09123378099030873601

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

6.348 × 10⁹⁴(95-digit number)

63488375345421970008…18246756198061747199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.348 × 10⁹⁴(95-digit number)

63488375345421970008…18246756198061747201

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

1.269 × 10⁹⁵(96-digit number)

12697675069084394001…36493512396123494399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.269 × 10⁹⁵(96-digit number)

12697675069084394001…36493512396123494401

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

2.539 × 10⁹⁵(96-digit number)

25395350138168788003…72987024792246988799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.539 × 10⁹⁵(96-digit number)

25395350138168788003…72987024792246988801

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

5.079 × 10⁹⁵(96-digit number)

50790700276337576006…45974049584493977599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.079 × 10⁹⁵(96-digit number)

50790700276337576006…45974049584493977601

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

1.015 × 10⁹⁶(97-digit number)

10158140055267515201…91948099168987955199

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 #665,372

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