Block #3,499,111

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/3/2020, 11:21:00 PM · Difficulty 10.9354 · 3,334,505 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ae69e9d9f29350340c30a884490ee172724f85f95bb994beb7286c8fe9fb5bf8

View on Chainz ↗

Height

#3,499,111

Difficulty

10.935442

Transactions

Size

902 B

Version

Bits

0aef791a

Nonce

407,713,273

Timestamp

1/3/2020, 11:21:00 PM

Confirmations

3,334,505

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

998ae3208cf5de12b60485c638d15c42b8fcb36032119a5cb70aebda7327aeb2

Transactions (2)

Coinbase037a954fa30876…f68a51e636866e

1 in → 1 out8.5000 XPM110 B

ASiq2qtK…VMhmk7yL

5f62392e70ed26…56e02a4c0d5324

1 in → 16 out199999.8500 XPM701 B

AU4f4km9…u8UnNcJ8 Ae8ZGyD5…tJBTVTnu ASPCJ5Zg…xJzds9AL AMFsu33L…cqBxewbK AP2ikm3r…2qJRNrn6

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.

1.838 × 10⁹⁷(98-digit number)

18385245894239707520…44766206275399874559

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

1.838 × 10⁹⁷(98-digit number)

18385245894239707520…44766206275399874559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.838 × 10⁹⁷(98-digit number)

18385245894239707520…44766206275399874561

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

3.677 × 10⁹⁷(98-digit number)

36770491788479415040…89532412550799749119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.677 × 10⁹⁷(98-digit number)

36770491788479415040…89532412550799749121

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

7.354 × 10⁹⁷(98-digit number)

73540983576958830080…79064825101599498239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.354 × 10⁹⁷(98-digit number)

73540983576958830080…79064825101599498241

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

1.470 × 10⁹⁸(99-digit number)

14708196715391766016…58129650203198996479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.470 × 10⁹⁸(99-digit number)

14708196715391766016…58129650203198996481

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

2.941 × 10⁹⁸(99-digit number)

29416393430783532032…16259300406397992959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.941 × 10⁹⁸(99-digit number)

29416393430783532032…16259300406397992961

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 #3,499,111

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