Block #501,831

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/20/2014, 1:07:27 AM · Difficulty 10.8051 · 6,316,194 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

845696ad80a6383a408a89bb696262119f8171d052f2cf9e00bf9fde84ebbced

View on Chainz ↗

Height

#501,831

Difficulty

10.805140

Transactions

Size

1.52 KB

Version

Bits

0ace1da1

Nonce

9,040

Timestamp

4/20/2014, 1:07:27 AM

Confirmations

6,316,194

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

9224109d088340d5dd1ff08b8dbf874d638285e5fd76a4a80efdfa2ba6a4adcf

Transactions (5)

Coinbase9e2d4ff856abe7…d538a36de4fd73

1 in → 1 out8.5900 XPM116 B

AbwWkWZt…kawDhufa

be14bebf8f084e…fe282014387cd9

4 in → 2 out31.9301 XPM669 B

AHZkUHtR…EUjZu7Tf AXgYGRfo…j5yqDDyE

41fbdc7ceaf328…f5268edb195fff

1 in → 2 out7.1150 XPM225 B

AJggGBSF…ioWg4H8E Adzfh93P…g4C99WV5

fda194f36deb5f…5bebe98fa6c421

1 in → 2 out7.0465 XPM226 B

AFuRfB4W…5g3FHF5t AcBdsJ3i…Fp5ntmLt

afca8ec9c95d74…21ebf5a7214337

1 in → 2 out6.4766 XPM227 B

ANsZYAZy…wSk4mkms AN65cSfZ…uVCirQsS

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.

4.065 × 10⁹⁷(98-digit number)

40657327691736704483…03053174950292385999

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

4.065 × 10⁹⁷(98-digit number)

40657327691736704483…03053174950292385999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.065 × 10⁹⁷(98-digit number)

40657327691736704483…03053174950292386001

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

8.131 × 10⁹⁷(98-digit number)

81314655383473408966…06106349900584771999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.131 × 10⁹⁷(98-digit number)

81314655383473408966…06106349900584772001

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

1.626 × 10⁹⁸(99-digit number)

16262931076694681793…12212699801169543999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.626 × 10⁹⁸(99-digit number)

16262931076694681793…12212699801169544001

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

3.252 × 10⁹⁸(99-digit number)

32525862153389363586…24425399602339087999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.252 × 10⁹⁸(99-digit number)

32525862153389363586…24425399602339088001

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

6.505 × 10⁹⁸(99-digit number)

65051724306778727172…48850799204678175999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.505 × 10⁹⁸(99-digit number)

65051724306778727172…48850799204678176001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.301 × 10⁹⁹(100-digit number)

13010344861355745434…97701598409356351999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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

Block #501,831

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