Block #1,619,393

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/8/2016, 12:43:29 PM · Difficulty 10.5890 · 5,196,582 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4c19626bb0a972411e79bc8c05b6bd81e1d0a5d1de8035182c80a423e80f8cdc

View on Chainz ↗

Height

#1,619,393

Difficulty

10.589009

Transactions

Size

120.26 KB

Version

Bits

0a96c946

Nonce

310,670,148

Timestamp

6/8/2016, 12:43:29 PM

Confirmations

5,196,582

Mined by

⛏️ P2SHAcJ2HcnV6pSSkpKezfTMW6w2Mbv9UVwzSN

Merkle Root

ca711c79851020cbe15615d3dd9894a37a1b6614a2644114f2cd4ac49aa07fc4

Transactions (3)

Coinbase3a38ee446678af…df5a6f4bdae20d

1 in → 1 out10.1600 XPM109 B

AcJ2HcnV…v9UVwzSN

b9211be68289c1…e956616f895d52

553 in → 1 out20.0000 XPM79.98 KB

AVsfGTte…niXFpmPh

283a393c5239ca…d6ccce18667433

277 in → 1 out10.0000 XPM40.09 KB

AGyiGjWR…yy2Gk1HV

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.

2.745 × 10⁹⁷(98-digit number)

27457623946073457467…76593381530602782719

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

2.745 × 10⁹⁷(98-digit number)

27457623946073457467…76593381530602782719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.745 × 10⁹⁷(98-digit number)

27457623946073457467…76593381530602782721

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

5.491 × 10⁹⁷(98-digit number)

54915247892146914935…53186763061205565439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.491 × 10⁹⁷(98-digit number)

54915247892146914935…53186763061205565441

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

1.098 × 10⁹⁸(99-digit number)

10983049578429382987…06373526122411130879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.098 × 10⁹⁸(99-digit number)

10983049578429382987…06373526122411130881

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

2.196 × 10⁹⁸(99-digit number)

21966099156858765974…12747052244822261759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.196 × 10⁹⁸(99-digit number)

21966099156858765974…12747052244822261761

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

4.393 × 10⁹⁸(99-digit number)

43932198313717531948…25494104489644523519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.393 × 10⁹⁸(99-digit number)

43932198313717531948…25494104489644523521

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 #1,619,393

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