Block #1,586,690

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/16/2016, 6:10:56 AM · Difficulty 10.6488 · 5,230,772 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fd5ea513842594887cbdd8a4bf81b80b8b07d75002b411a35064c6174b2c0192

View on Chainz ↗

Height

#1,586,690

Difficulty

10.648753

Transactions

Size

868 B

Version

Bits

0aa614a7

Nonce

825,011,555

Timestamp

5/16/2016, 6:10:56 AM

Confirmations

5,230,772

Mined by

⛏️ P2SHAbqaByzRQsZzfcVmZWPjKqoxPXF6XniZHm

Merkle Root

267b03beada229277ec01f55e7a8506bf0c82137e47ecd169100b167efffcf40

Transactions (2)

Coinbasee49b1d447cc494…ce175a82758f9f

1 in → 1 out8.8100 XPM109 B

AbqaByzR…F6XniZHm

0e82baeebf479b…ad5f36c35038e4

1 in → 15 out42.2461 XPM668 B

AKiS3exQ…NXWwP1Mq AQ7nZY3N…fkJULpfe AbwijVU5…qRbvEC24 AeXndF8L…VYjXuwhk Ab7YJgF5…GXWvbwCd

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.

1.929 × 10⁹⁷(98-digit number)

19293185302772545746…01520848185041960959

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

1.929 × 10⁹⁷(98-digit number)

19293185302772545746…01520848185041960959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.929 × 10⁹⁷(98-digit number)

19293185302772545746…01520848185041960961

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

3.858 × 10⁹⁷(98-digit number)

38586370605545091493…03041696370083921919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.858 × 10⁹⁷(98-digit number)

38586370605545091493…03041696370083921921

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

7.717 × 10⁹⁷(98-digit number)

77172741211090182987…06083392740167843839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.717 × 10⁹⁷(98-digit number)

77172741211090182987…06083392740167843841

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

1.543 × 10⁹⁸(99-digit number)

15434548242218036597…12166785480335687679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.543 × 10⁹⁸(99-digit number)

15434548242218036597…12166785480335687681

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

3.086 × 10⁹⁸(99-digit number)

30869096484436073194…24333570960671375359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.086 × 10⁹⁸(99-digit number)

30869096484436073194…24333570960671375361

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 #1,586,690

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