Block #246,635

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/6/2013, 6:47:42 AM · Difficulty 9.9642 · 6,578,557 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f6ca1fbe7267aea481d06bbf0db044b97395207f07413358d880b450811222bf

View on Chainz ↗

Height

#246,635

Difficulty

9.964212

Transactions

Size

69.38 KB

Version

Bits

09f6d699

Nonce

27,006

Timestamp

11/6/2013, 6:47:42 AM

Confirmations

6,578,557

Mined by

⛏️ P2SHARmAMwyuAi8euPwQcDptyGopF9P7Kn74ZT

Merkle Root

56c9857c6b53f362dceefe365ee85f53dcaeaeadb484ba84b68ffe400eef0514

Transactions (2)

Coinbase081d7a8da64860…4429e98def5c36

1 in → 2 out10.7700 XPM137 B

ARmAMwyu…P7Kn74ZT AU6kq4CL…dQBLvxLp

920e5658f5e613…77ab97339c59a0

478 in → 2 out97.4248 XPM69.16 KB

AS6XvSSg…voTjh9Mw AeAqa25d…YB5jxSAa

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.

9.059 × 10⁹⁸(99-digit number)

90590966726346868564…44789524081607772159

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

9.059 × 10⁹⁸(99-digit number)

90590966726346868564…44789524081607772159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.059 × 10⁹⁸(99-digit number)

90590966726346868564…44789524081607772161

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

1.811 × 10⁹⁹(100-digit number)

18118193345269373712…89579048163215544319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.811 × 10⁹⁹(100-digit number)

18118193345269373712…89579048163215544321

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

3.623 × 10⁹⁹(100-digit number)

36236386690538747425…79158096326431088639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.623 × 10⁹⁹(100-digit number)

36236386690538747425…79158096326431088641

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

7.247 × 10⁹⁹(100-digit number)

72472773381077494851…58316192652862177279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.247 × 10⁹⁹(100-digit number)

72472773381077494851…58316192652862177281

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

1.449 × 10¹⁰⁰(101-digit number)

14494554676215498970…16632385305724354559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.449 × 10¹⁰⁰(101-digit number)

14494554676215498970…16632385305724354561

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

2.898 × 10¹⁰⁰(101-digit number)

28989109352430997940…33264770611448709119

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 #246,635

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