Block #2,726,195

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/29/2018, 5:11:28 AM · Difficulty 11.6242 · 4,104,854 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5a187504f0af6c78598edbaf0257d017527f257f9583bd12ad38b9ee786b1999

View on Chainz ↗

Height

#2,726,195

Difficulty

11.624155

Transactions

Size

2.01 KB

Version

Bits

0b9fc8a6

Nonce

1,558,194,516

Timestamp

6/29/2018, 5:11:28 AM

Confirmations

4,104,854

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

c7fa050bfdd548a157e2539951cd5ee53793eb979bd3b792a85b97ff19f844f8

Transactions (4)

Coinbase45d399313628f3…14bc8e54d65c35

1 in → 1 out7.4200 XPM110 B

AZtxQr2F…7grUWrUz

53629ed4f54b30…8fc41aa9bb428b

3 in → 2 out673.6005 XPM522 B

AQmjqzoU…5U6sbve9 AKUM4r7D…9MxfAfMD

39bf787e461d7a…eded44d52c0397

5 in → 2 out136.2017 XPM819 B

AbWUUvcW…Gpi5ctLQ AQmjqzoU…5U6sbve9

6d17e60e0f6859…091cfea8445b2a

3 in → 2 out7.2627 XPM520 B

AZgwUXVh…4zzSLxPQ AJDTRKPA…PspAqsan

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.

1.954 × 10⁹⁷(98-digit number)

19549310546099067527…58388506387512944639

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

1.954 × 10⁹⁷(98-digit number)

19549310546099067527…58388506387512944639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.954 × 10⁹⁷(98-digit number)

19549310546099067527…58388506387512944641

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

3.909 × 10⁹⁷(98-digit number)

39098621092198135054…16777012775025889279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.909 × 10⁹⁷(98-digit number)

39098621092198135054…16777012775025889281

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

7.819 × 10⁹⁷(98-digit number)

78197242184396270108…33554025550051778559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.819 × 10⁹⁷(98-digit number)

78197242184396270108…33554025550051778561

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

1.563 × 10⁹⁸(99-digit number)

15639448436879254021…67108051100103557119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.563 × 10⁹⁸(99-digit number)

15639448436879254021…67108051100103557121

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

3.127 × 10⁹⁸(99-digit number)

31278896873758508043…34216102200207114239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.127 × 10⁹⁸(99-digit number)

31278896873758508043…34216102200207114241

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

6.255 × 10⁹⁸(99-digit number)

62557793747517016086…68432204400414228479

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 #2,726,195

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