Block #3,062,760

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/21/2019, 3:21:21 PM · Difficulty 11.0103 · 3,775,873 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

db36fd3f460d705a9d85af191579852da315ee2c5305c8dffb8b55794264e447

View on Chainz ↗

Height

#3,062,760

Difficulty

11.010350

Transactions

Size

722 B

Version

Bits

0b02a648

Nonce

1,163,035,420

Timestamp

2/21/2019, 3:21:21 PM

Confirmations

3,775,873

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

d2f0040bfcbe121c105241751c68d98d41002972874f90ba18ae4957b63b24b2

Transactions (2)

Coinbasef865700abad58a…41af3c4aaf7083

1 in → 1 out8.2500 XPM110 B

AUhjokok…k5m93PZR

5a0bd66b88605c…eebdad211182e6

3 in → 2 out731.9484 XPM521 B

AeTHTL7A…vT1872bk AURtWWBi…HYjjmHTG

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.

5.859 × 10⁹⁷(98-digit number)

58591332332134180704…43517393790453944319

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

5.859 × 10⁹⁷(98-digit number)

58591332332134180704…43517393790453944319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.859 × 10⁹⁷(98-digit number)

58591332332134180704…43517393790453944321

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

1.171 × 10⁹⁸(99-digit number)

11718266466426836140…87034787580907888639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.171 × 10⁹⁸(99-digit number)

11718266466426836140…87034787580907888641

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

2.343 × 10⁹⁸(99-digit number)

23436532932853672281…74069575161815777279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.343 × 10⁹⁸(99-digit number)

23436532932853672281…74069575161815777281

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

4.687 × 10⁹⁸(99-digit number)

46873065865707344563…48139150323631554559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.687 × 10⁹⁸(99-digit number)

46873065865707344563…48139150323631554561

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

9.374 × 10⁹⁸(99-digit number)

93746131731414689127…96278300647263109119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.374 × 10⁹⁸(99-digit number)

93746131731414689127…96278300647263109121

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

1.874 × 10⁹⁹(100-digit number)

18749226346282937825…92556601294526218239

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 #3,062,760

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