Block #922,364

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 10:18:00 AM · Difficulty 10.9155 · 5,869,823 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7ccb0ee176eaacb3a34adedf7a5cd77cec55e6a6f1d2b3d8a13386ae4a6e3f18

View on Chainz ↗

Height

#922,364

Difficulty

10.915535

Transactions

Size

115.99 KB

Version

Bits

0aea607e

Nonce

301,252,476

Timestamp

2/4/2015, 10:18:00 AM

Confirmations

5,869,823

Merkle Root

0312f8c429304dab692697bc53f47181d697b44f7c5cab04247c3b8599400f3b

Transactions (5)

Coinbasea2de437774c865…dcd4de6129fcc4

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

dba1a59d66b878…4be8f39cde6f99

200 in → 1 out1126.2826 XPM28.95 KB

AKuP4XsJ…owbodNxQ

b5db449886e9e2…b6c1f92d16caea

200 in → 1 out864.1711 XPM28.95 KB

AKuP4XsJ…owbodNxQ

aa0e8862da1f12…4f32b2e3fe850c

200 in → 1 out1038.7297 XPM28.95 KB

AKuP4XsJ…owbodNxQ

3d1f3f026a7451…08d877b07552db

200 in → 1 out1102.9304 XPM28.95 KB

AKuP4XsJ…owbodNxQ

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.

3.686 × 10⁹⁶(97-digit number)

36862146039621377100…22607951376258429439

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

3.686 × 10⁹⁶(97-digit number)

36862146039621377100…22607951376258429439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.686 × 10⁹⁶(97-digit number)

36862146039621377100…22607951376258429441

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

7.372 × 10⁹⁶(97-digit number)

73724292079242754200…45215902752516858879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.372 × 10⁹⁶(97-digit number)

73724292079242754200…45215902752516858881

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

1.474 × 10⁹⁷(98-digit number)

14744858415848550840…90431805505033717759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.474 × 10⁹⁷(98-digit number)

14744858415848550840…90431805505033717761

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

2.948 × 10⁹⁷(98-digit number)

29489716831697101680…80863611010067435519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.948 × 10⁹⁷(98-digit number)

29489716831697101680…80863611010067435521

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

5.897 × 10⁹⁷(98-digit number)

58979433663394203360…61727222020134871039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.897 × 10⁹⁷(98-digit number)

58979433663394203360…61727222020134871041

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