Block #290,860

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/2/2013, 9:40:19 PM · Difficulty 9.9895 · 6,508,501 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

adc43c386003f456ba524c2b3d816169fe52e7088a0273d76a00391246c1e816

View on Chainz ↗

Height

#290,860

Difficulty

9.989510

Transactions

Size

1.15 KB

Version

Bits

09fd508a

Nonce

42,666

Timestamp

12/2/2013, 9:40:19 PM

Confirmations

6,508,501

Mined by

⛏️ ,paRAZninDSu1Gy3NdWkaTGfLDa2i9FvgDMwC4

Merkle Root

aef5feec4d2dda5c3f1b109096c8ecdeb893b145136aa27bdeaa1448a5301b0b

Transactions (1)

Coinbaseaef5feec4d2dda…aa1448a5301b0b

1 in → 30 out9.9900 XPM1.06 KB

AZninDSu…FvgDMwC4 AYcLTeXR…bscgPops AWXYBWKP…qQAoisBJ AQwRN8bE…V8PsTcY9 AVss9H5F…zXhyMijY

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.

1.082 × 10¹⁰⁰(101-digit number)

10828050533453042758…21082837135044317299

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

1.082 × 10¹⁰⁰(101-digit number)

10828050533453042758…21082837135044317299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.082 × 10¹⁰⁰(101-digit number)

10828050533453042758…21082837135044317301

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

2.165 × 10¹⁰⁰(101-digit number)

21656101066906085517…42165674270088634599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.165 × 10¹⁰⁰(101-digit number)

21656101066906085517…42165674270088634601

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

4.331 × 10¹⁰⁰(101-digit number)

43312202133812171034…84331348540177269199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.331 × 10¹⁰⁰(101-digit number)

43312202133812171034…84331348540177269201

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

8.662 × 10¹⁰⁰(101-digit number)

86624404267624342068…68662697080354538399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.662 × 10¹⁰⁰(101-digit number)

86624404267624342068…68662697080354538401

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

1.732 × 10¹⁰¹(102-digit number)

17324880853524868413…37325394160709076799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.732 × 10¹⁰¹(102-digit number)

17324880853524868413…37325394160709076801

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