Block #3,668,710

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/3/2020, 12:25:35 AM · Difficulty 10.8840 · 3,141,669 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5b5e140bd7aab11e6dfb76f20079b57053a7a5100a63f7ee8ce1b55802f72c79

View on Chainz ↗

Height

#3,668,710

Difficulty

10.884043

Transactions

Size

3.94 KB

Version

Bits

0ae250aa

Nonce

29,394,961

Timestamp

5/3/2020, 12:25:35 AM

Confirmations

3,141,669

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

545bcf737abf6d10273d8fdf3d2d1fc2d6e8192cc2f9c9595298f2abf4acc8ff

Transactions (5)

Coinbase2c5ece56fbd248…4e513042357b62

1 in → 1 out8.4900 XPM110 B

ASiq2qtK…VMhmk7yL

a10027a7e65fe4…9e10e4105fdf3b

24 in → 2 out202.2900 XPM2.75 KB

ASiq2qtK…VMhmk7yL AV6uiSpn…mVtYMk4T

049df2cb5781ff…82bf45868aed6e

2 in → 2 out16.8500 XPM305 B

ASiq2qtK…VMhmk7yL AWxHVeWs…Q7RMs542

41c9a1b603b0f3…048238b5bb57a8

2 in → 2 out11.8979 XPM342 B

ASiq2qtK…VMhmk7yL AP2ikm3r…2qJRNrn6

00f071252b1a51…fbe3716e036fb8

2 in → 2 out1.1668 XPM373 B

AUA38Ys3…uBfJ1V6B 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.

5.439 × 10⁹⁶(97-digit number)

54399811967525775258…39949758625096775679

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

5.439 × 10⁹⁶(97-digit number)

54399811967525775258…39949758625096775679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.439 × 10⁹⁶(97-digit number)

54399811967525775258…39949758625096775681

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

1.087 × 10⁹⁷(98-digit number)

10879962393505155051…79899517250193551359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.087 × 10⁹⁷(98-digit number)

10879962393505155051…79899517250193551361

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

2.175 × 10⁹⁷(98-digit number)

21759924787010310103…59799034500387102719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.175 × 10⁹⁷(98-digit number)

21759924787010310103…59799034500387102721

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

4.351 × 10⁹⁷(98-digit number)

43519849574020620206…19598069000774205439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.351 × 10⁹⁷(98-digit number)

43519849574020620206…19598069000774205441

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

8.703 × 10⁹⁷(98-digit number)

87039699148041240413…39196138001548410879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.703 × 10⁹⁷(98-digit number)

87039699148041240413…39196138001548410881

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

1.740 × 10⁹⁸(99-digit number)

17407939829608248082…78392276003096821759

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 #3,668,710

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