Block #461,846

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/27/2014, 12:34:14 AM · Difficulty 10.4146 · 6,337,186 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fa4638485b51ea44b65685c005ece6584d76f229501497b467e6fad00d2809bd

View on Chainz ↗

Height

#461,846

Difficulty

10.414577

Transactions

Size

15.95 KB

Version

Bits

0a6a21b9

Nonce

47,287,910

Timestamp

3/27/2014, 12:34:14 AM

Confirmations

6,337,186

Mined by

⛏️ P2SHAdrBCXEBPNG1UaQpygdJDh42im4P1sUxat

Merkle Root

c6f2b4bafe325de4b425078c23c389f783e60886067a6c4e3e3f596a1c12e658

Transactions (5)

Coinbase3f648069fe945c…7577fc56732a3f

1 in → 1 out9.3900 XPM110 B

AdrBCXEB…4P1sUxat

dc1c59a9106d12…4105ee4f4d4ed7

38 in → 2 out145.6475 XPM5.57 KB

ALtJtqc8…mfHp46Qy AGqVscE3…tKXBQ5BN

7f9862cdf15562…2f9f24650772e2

56 in → 2 out145.0100 XPM8.17 KB

AWE9PRsf…8hBg43u1 AajiE5fj…h7ap2EQ7

ab36008dc7a3de…90271426953819

7 in → 24 out46.3266 XPM1.82 KB

Aepo3mhd…AwoPnjG3 AUkdqaxr…4jcbMUQ7 AN2bt7kX…xXcnV5eU AZpAKTCH…4zW8jaa9 ARCcAJFk…XQA5j6C5

7d24401c1422f2…8dc98d117e08b8

1 in → 1 out2.9978 XPM192 B

AQycRJyi…Xxv2YYPe

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.

4.970 × 10⁹⁷(98-digit number)

49705673670748899633…16483407719950479359

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

4.970 × 10⁹⁷(98-digit number)

49705673670748899633…16483407719950479359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.970 × 10⁹⁷(98-digit number)

49705673670748899633…16483407719950479361

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

9.941 × 10⁹⁷(98-digit number)

99411347341497799266…32966815439900958719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.941 × 10⁹⁷(98-digit number)

99411347341497799266…32966815439900958721

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

1.988 × 10⁹⁸(99-digit number)

19882269468299559853…65933630879801917439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.988 × 10⁹⁸(99-digit number)

19882269468299559853…65933630879801917441

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

3.976 × 10⁹⁸(99-digit number)

39764538936599119706…31867261759603834879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.976 × 10⁹⁸(99-digit number)

39764538936599119706…31867261759603834881

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

7.952 × 10⁹⁸(99-digit number)

79529077873198239412…63734523519207669759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.952 × 10⁹⁸(99-digit number)

79529077873198239412…63734523519207669761

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