Block #3,339,390

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/3/2019, 4:01:07 PM · Difficulty 11.0034 · 3,501,352 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b43ac8c23cd74e83ed360d8fd0f39f2429ec9090e4a7989760f76066cb340440

View on Chainz ↗

Height

#3,339,390

Difficulty

11.003407

Transactions

Size

1.69 KB

Version

Bits

0b00df50

Nonce

2,105,139,018

Timestamp

9/3/2019, 4:01:07 PM

Confirmations

3,501,352

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

6148e92bd841a3bb9d90c0b62537cbcfde5fcd18c20e22aa5146206d5b4998e9

Transactions (4)

Coinbase76fa1aa311228e…c1d1c2aef3df6b

1 in → 1 out8.2900 XPM110 B

ASiq2qtK…VMhmk7yL

10fd8ee6926862…65161edab586a7

6 in → 2 out10.0697 XPM931 B

AVRgvCv8…PqzQYmPk ASiq2qtK…VMhmk7yL

644c227dd30a05…6e95309273ed89

2 in → 2 out8.0130 XPM373 B

AeTHTL7A…vT1872bk AMAiUsof…DKAF9VWT

2d31d3ce31c4d5…aa28175d5e4735

1 in → 2 out6.4755 XPM225 B

AWaYC9BA…1BzTFe5J ASiq2qtK…VMhmk7yL

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.

3.556 × 10⁹⁵(96-digit number)

35566627143491743409…04806784389698171599

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

3.556 × 10⁹⁵(96-digit number)

35566627143491743409…04806784389698171599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.556 × 10⁹⁵(96-digit number)

35566627143491743409…04806784389698171601

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

7.113 × 10⁹⁵(96-digit number)

71133254286983486818…09613568779396343199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.113 × 10⁹⁵(96-digit number)

71133254286983486818…09613568779396343201

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

1.422 × 10⁹⁶(97-digit number)

14226650857396697363…19227137558792686399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.422 × 10⁹⁶(97-digit number)

14226650857396697363…19227137558792686401

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

2.845 × 10⁹⁶(97-digit number)

28453301714793394727…38454275117585372799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.845 × 10⁹⁶(97-digit number)

28453301714793394727…38454275117585372801

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

5.690 × 10⁹⁶(97-digit number)

56906603429586789455…76908550235170745599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.690 × 10⁹⁶(97-digit number)

56906603429586789455…76908550235170745601

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

1.138 × 10⁹⁷(98-digit number)

11381320685917357891…53817100470341491199

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 #3,339,390

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