Block #3,086,691

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/10/2019, 9:37:09 AM · Difficulty 11.0379 · 3,755,856 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c117a22bbf620098d3762fabce05986e7c94d1c86a59a5f222f49f52750924da

View on Chainz ↗

Height

#3,086,691

Difficulty

11.037894

Transactions

Size

1.76 KB

Version

Bits

0b09b36b

Nonce

285,446,502

Timestamp

3/10/2019, 9:37:09 AM

Confirmations

3,755,856

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

f4dad9027587d041b6049861a369b7b745deacb58f7112b61ea9df15d8c05d6b

Transactions (3)

Coinbasec72d2eddf796fa…bbd537c87c7705

1 in → 1 out8.2200 XPM110 B

AbXwmGxD…4XXYP765

ed749a3b86b379…a8e2cf65494b0f

5 in → 2 out37.8710 XPM818 B

AZQgL5kt…6NE43uZs AdNfCgx9…Ho27G1iT

41caf12d0b37a0…b5474caab1c1c3

5 in → 2 out10.0261 XPM787 B

ANSyufnk…Z5GdxVnm AbXwmGxD…4XXYP765

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.

1.349 × 10⁹⁹(100-digit number)

13497121909957406349…86090901572857446399

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

1.349 × 10⁹⁹(100-digit number)

13497121909957406349…86090901572857446399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.349 × 10⁹⁹(100-digit number)

13497121909957406349…86090901572857446401

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

2.699 × 10⁹⁹(100-digit number)

26994243819914812699…72181803145714892799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.699 × 10⁹⁹(100-digit number)

26994243819914812699…72181803145714892801

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

5.398 × 10⁹⁹(100-digit number)

53988487639829625398…44363606291429785599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.398 × 10⁹⁹(100-digit number)

53988487639829625398…44363606291429785601

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

1.079 × 10¹⁰⁰(101-digit number)

10797697527965925079…88727212582859571199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.079 × 10¹⁰⁰(101-digit number)

10797697527965925079…88727212582859571201

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

2.159 × 10¹⁰⁰(101-digit number)

21595395055931850159…77454425165719142399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.159 × 10¹⁰⁰(101-digit number)

21595395055931850159…77454425165719142401

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

4.319 × 10¹⁰⁰(101-digit number)

43190790111863700318…54908850331438284799

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 #3,086,691

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