Block #919,824

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/2/2015, 11:53:10 AM · Difficulty 10.9195 · 5,883,785 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a022aa2ad62036e2b11b18651719127f61d63072e58723d22f99d2081ef3832e

View on Chainz ↗

Height

#919,824

Difficulty

10.919470

Transactions

Size

1.14 KB

Version

Bits

0aeb6266

Nonce

777,286,406

Timestamp

2/2/2015, 11:53:10 AM

Confirmations

5,883,785

Mined by

⛏️ P2SHAXGjD9ezPcpjTVDFQwXWZXL8vYnZg5mMTs

Merkle Root

b22ea1ebdce424652171fc2b3cd6bfc2ddcc94d2076bdc38b3c33ff3c10ce970

Transactions (2)

Coinbasedc374de8343f8a…1f8e3a4da38195

1 in → 1 out8.4000 XPM109 B

AXGjD9ez…nZg5mMTs

dd92c8ab0ba6e5…37583cba2f3b84

6 in → 2 out1008.1861 XPM965 B

ARCfvxEY…tAAsnRYd AUSxVrre…B27XD3yv

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.

6.816 × 10⁹⁴(95-digit number)

68163627612866624333…25238797907055963199

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

6.816 × 10⁹⁴(95-digit number)

68163627612866624333…25238797907055963199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.816 × 10⁹⁴(95-digit number)

68163627612866624333…25238797907055963201

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

1.363 × 10⁹⁵(96-digit number)

13632725522573324866…50477595814111926399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.363 × 10⁹⁵(96-digit number)

13632725522573324866…50477595814111926401

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

2.726 × 10⁹⁵(96-digit number)

27265451045146649733…00955191628223852799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.726 × 10⁹⁵(96-digit number)

27265451045146649733…00955191628223852801

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

5.453 × 10⁹⁵(96-digit number)

54530902090293299466…01910383256447705599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.453 × 10⁹⁵(96-digit number)

54530902090293299466…01910383256447705601

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

1.090 × 10⁹⁶(97-digit number)

10906180418058659893…03820766512895411199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.090 × 10⁹⁶(97-digit number)

10906180418058659893…03820766512895411201

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