Block #1,463,770

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/19/2016, 5:17:13 AM · Difficulty 10.7789 · 5,377,735 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

92effa61835aac851400d6cbd1f3d543ab49b4896634c9d5b97e893299efa950

View on Chainz ↗

Height

#1,463,770

Difficulty

10.778923

Transactions

Size

2.92 KB

Version

Bits

0ac76782

Nonce

642,823,892

Timestamp

2/19/2016, 5:17:13 AM

Confirmations

5,377,735

Mined by

⛏️ P2SHAd83BSvDHvj9wLCf6t13joMXvjKsJGZmAm

Merkle Root

844511daf8de4b3a858264607fd3ffbd2a87bf2a0ed0c80816068fcbf538b93b

Transactions (3)

Coinbase3245e3bd0e7a88…e106390731f95e

1 in → 1 out8.7000 XPM110 B

Ad83BSvD…KsJGZmAm

89c03e7f283f4d…d237197290539d

11 in → 2 out1000000.0100 XPM1.67 KB

AZNjRVbV…q4fSKXrT ATNFg4tq…AMdaKJFH

a97612f00bd995…0c2ed91d6fbbf6

7 in → 1 out27.9800 XPM1.05 KB

AQVNVjFK…BBBxJVUq

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.

2.894 × 10⁹⁸(99-digit number)

28941395790776448331…69115533852224716799

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

2.894 × 10⁹⁸(99-digit number)

28941395790776448331…69115533852224716799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.894 × 10⁹⁸(99-digit number)

28941395790776448331…69115533852224716801

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

5.788 × 10⁹⁸(99-digit number)

57882791581552896663…38231067704449433599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.788 × 10⁹⁸(99-digit number)

57882791581552896663…38231067704449433601

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

1.157 × 10⁹⁹(100-digit number)

11576558316310579332…76462135408898867199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.157 × 10⁹⁹(100-digit number)

11576558316310579332…76462135408898867201

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

2.315 × 10⁹⁹(100-digit number)

23153116632621158665…52924270817797734399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.315 × 10⁹⁹(100-digit number)

23153116632621158665…52924270817797734401

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

4.630 × 10⁹⁹(100-digit number)

46306233265242317330…05848541635595468799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.630 × 10⁹⁹(100-digit number)

46306233265242317330…05848541635595468801

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

Block #1,463,770

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