Block #3,412,474

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/30/2019, 6:52:55 AM · Difficulty 10.9850 · 3,425,968 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

82714a4f693d74cc594651501dff2f4e52d24397b49c5ddaaae3688467be782e

View on Chainz ↗

Height

#3,412,474

Difficulty

10.984961

Transactions

Size

7.35 KB

Version

Bits

0afc2662

Nonce

817,630,263

Timestamp

10/30/2019, 6:52:55 AM

Confirmations

3,425,968

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

3819f7a842c1a3120c8c3aaad89ec1e1cb8bdd506508abfe79ff00890c558cf5

Transactions (2)

Coinbasedfad009eb7c298…cc6dc7b0131d48

1 in → 1 out8.3500 XPM109 B

ASiq2qtK…VMhmk7yL

4373658ca435ce…6bb0930414e3c0

49 in → 2 out4827.0000 XPM7.16 KB

ASgveuFC…Kf7cceMD AX3W6pJy…NwZ88svU

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.

2.287 × 10⁹⁵(96-digit number)

22877455148140545288…26032512277660559359

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

2.287 × 10⁹⁵(96-digit number)

22877455148140545288…26032512277660559359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.287 × 10⁹⁵(96-digit number)

22877455148140545288…26032512277660559361

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

4.575 × 10⁹⁵(96-digit number)

45754910296281090576…52065024555321118719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.575 × 10⁹⁵(96-digit number)

45754910296281090576…52065024555321118721

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

9.150 × 10⁹⁵(96-digit number)

91509820592562181152…04130049110642237439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.150 × 10⁹⁵(96-digit number)

91509820592562181152…04130049110642237441

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

1.830 × 10⁹⁶(97-digit number)

18301964118512436230…08260098221284474879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.830 × 10⁹⁶(97-digit number)

18301964118512436230…08260098221284474881

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

3.660 × 10⁹⁶(97-digit number)

36603928237024872460…16520196442568949759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.660 × 10⁹⁶(97-digit number)

36603928237024872460…16520196442568949761

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

7.320 × 10⁹⁶(97-digit number)

73207856474049744921…33040392885137899519

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 #3,412,474

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