Block #1,406,466

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/9/2016, 9:48:44 PM · Difficulty 10.8075 · 5,430,049 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

978fe8d788ab89736ed209be260c98a67038b7c8094cabfa458195ecd20c0bcc

View on Chainz ↗

Height

#1,406,466

Difficulty

10.807481

Transactions

Size

2.04 KB

Version

Bits

0aceb71b

Nonce

1,245,751,887

Timestamp

1/9/2016, 9:48:44 PM

Confirmations

5,430,049

Mined by

⛏️ P2SHAQLTxsQ6r74A2TyjYX5ywYy3mPXDfT9qvZ

Merkle Root

c30dbc9e11db654057c6ec64a83e4305ba431616390d108a8a9ce1769d86e76a

Transactions (2)

Coinbase451cc1d1fe2fc1…d1ac3ef82009f8

1 in → 1 out8.5700 XPM109 B

AQLTxsQ6…XDfT9qvZ

24e0f44441b3ab…cdb3d01a8e3ffc

1 in → 51 out8.7849 XPM1.85 KB

AHmLG7Ae…dQMc62HF AQz2Fnkq…akCg2WP4 AUhLZdsR…gKMfjeDb AXDorCDc…bfaGoaGv AH2vBEUd…duXkb2rm

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.

3.470 × 10⁹⁴(95-digit number)

34706261262861655581…81102803504423804839

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

3.470 × 10⁹⁴(95-digit number)

34706261262861655581…81102803504423804839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.470 × 10⁹⁴(95-digit number)

34706261262861655581…81102803504423804841

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

6.941 × 10⁹⁴(95-digit number)

69412522525723311163…62205607008847609679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.941 × 10⁹⁴(95-digit number)

69412522525723311163…62205607008847609681

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

1.388 × 10⁹⁵(96-digit number)

13882504505144662232…24411214017695219359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.388 × 10⁹⁵(96-digit number)

13882504505144662232…24411214017695219361

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

2.776 × 10⁹⁵(96-digit number)

27765009010289324465…48822428035390438719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.776 × 10⁹⁵(96-digit number)

27765009010289324465…48822428035390438721

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

5.553 × 10⁹⁵(96-digit number)

55530018020578648930…97644856070780877439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.553 × 10⁹⁵(96-digit number)

55530018020578648930…97644856070780877441

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 #1,406,466

Cookie Preferences