Block #466,748

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/30/2014, 8:57:52 AM · Difficulty 10.4260 · 6,338,950 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

675f36f15fb95787e49faebf8cbf199d6e95d88196c655de6f4dedfaad38bb22

View on Chainz ↗

Height

#466,748

Difficulty

10.425979

Transactions

Size

832 B

Version

Bits

0a6d0cfe

Nonce

2,667

Timestamp

3/30/2014, 8:57:52 AM

Confirmations

6,338,950

Mined by

⛏️ <aS7AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

3ce9a470b46834537499a934221d59cf5adc3ad9cdd59941a3796c9314446780

Transactions (1)

Coinbase3ce9a470b46834…796c9314446780

1 in → 20 out9.1884 XPM742 B

AQvZBsUo…hppgRZTJ ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn AJtNW28X…Syb4Ph5j AQyr8Lw3…hs4nt3Pn

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.

1.630 × 10⁹⁵(96-digit number)

16307368576218039660…45135111593662009999

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

1.630 × 10⁹⁵(96-digit number)

16307368576218039660…45135111593662009999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.630 × 10⁹⁵(96-digit number)

16307368576218039660…45135111593662010001

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

3.261 × 10⁹⁵(96-digit number)

32614737152436079321…90270223187324019999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.261 × 10⁹⁵(96-digit number)

32614737152436079321…90270223187324020001

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

6.522 × 10⁹⁵(96-digit number)

65229474304872158643…80540446374648039999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.522 × 10⁹⁵(96-digit number)

65229474304872158643…80540446374648040001

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

1.304 × 10⁹⁶(97-digit number)

13045894860974431728…61080892749296079999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.304 × 10⁹⁶(97-digit number)

13045894860974431728…61080892749296080001

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

2.609 × 10⁹⁶(97-digit number)

26091789721948863457…22161785498592159999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.609 × 10⁹⁶(97-digit number)

26091789721948863457…22161785498592160001

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