Block #219,798

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/20/2013, 4:53:57 PM · Difficulty 9.9341 · 6,572,665 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e61207c9b20735b293061fe289549f1f9a24345b1b54e7cb5930cfb5d01e5ccb

View on Chainz ↗

Height

#219,798

Difficulty

9.934113

Transactions

Size

801 B

Version

Bits

09ef220d

Nonce

7,811

Timestamp

10/20/2013, 4:53:57 PM

Confirmations

6,572,665

Merkle Root

6a56067392d6e303ebe210f299a34997edab086ea1c9167dc620add18a7c2d07

Transactions (3)

Coinbase4f74cf4b06153c…753bd87dda21cf

1 in → 1 out10.1400 XPM110 B

AYCiS6Hu…37auXKDN

458c068e36245c…adedeecdf95c14

2 in → 2 out4.2800 XPM374 B

AHBnwRV6…KyM4zwjU ASghXt3M…K8SZg33D

071dbfb0f01806…7af918c366a8f8

1 in → 2 out8.1093 XPM227 B

AVCXjFru…iBtRAfYK AeNo3RVm…WruQcTwE

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.

5.340 × 10⁹³(94-digit number)

53407647266815825323…26161921069020994559

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

5.340 × 10⁹³(94-digit number)

53407647266815825323…26161921069020994559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.340 × 10⁹³(94-digit number)

53407647266815825323…26161921069020994561

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

1.068 × 10⁹⁴(95-digit number)

10681529453363165064…52323842138041989119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.068 × 10⁹⁴(95-digit number)

10681529453363165064…52323842138041989121

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

2.136 × 10⁹⁴(95-digit number)

21363058906726330129…04647684276083978239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.136 × 10⁹⁴(95-digit number)

21363058906726330129…04647684276083978241

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

4.272 × 10⁹⁴(95-digit number)

42726117813452660258…09295368552167956479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.272 × 10⁹⁴(95-digit number)

42726117813452660258…09295368552167956481

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

8.545 × 10⁹⁴(95-digit number)

85452235626905320516…18590737104335912959

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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