Block #2,752,291

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/17/2018, 2:38:26 AM · Difficulty 11.6487 · 4,089,816 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f7b8d07f944cb4addbcfa815c9225460531d6d5e3547ae1b04b77d6410be13a7

View on Chainz ↗

Height

#2,752,291

Difficulty

11.648713

Transactions

Size

3.15 KB

Version

Bits

0ba61209

Nonce

343,548,422

Timestamp

7/17/2018, 2:38:26 AM

Confirmations

4,089,816

Mined by

⛏️ P2SHAPC7xuDrGvDPNnQWGPHdfDPP5Mj27vYweo

Merkle Root

84b3bb0f65c2f0b0d7ef34971a6254983422896689b756c70e9d9f5d742bba2e

Transactions (5)

Coinbase5ee9b45f8954c7…7b637f116dd717

1 in → 1 out7.4300 XPM110 B

APC7xuDr…j27vYweo

3fce6409e1d6e5…87191633ba3693

12 in → 2 out9930.8600 XPM1.81 KB

AKTeYnrd…6oLdSTP2 AUVDeswj…8LdCsnu4

2f432afe051947…89fe4f91502130

3 in → 2 out14.8305 XPM522 B

AGN85UQD…2vZvQZtu AFpHJhDK…hyA1PvSQ

0ad4ea4c417048…417f3ef9cfa3bc

2 in → 2 out14.7000 XPM307 B

AYGchnep…aKZEsSy4 AYvGxhg5…ZLbgzK6R

a69427b86f61da…1badeb762ffb28

2 in → 2 out12.0500 XPM339 B

AYcAkzMW…ab81tEp2 APVKWthF…PMMxwRoz

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.

7.120 × 10⁹⁴(95-digit number)

71202616869012971493…79545250854032087839

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

7.120 × 10⁹⁴(95-digit number)

71202616869012971493…79545250854032087839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.120 × 10⁹⁴(95-digit number)

71202616869012971493…79545250854032087841

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

1.424 × 10⁹⁵(96-digit number)

14240523373802594298…59090501708064175679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.424 × 10⁹⁵(96-digit number)

14240523373802594298…59090501708064175681

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

2.848 × 10⁹⁵(96-digit number)

28481046747605188597…18181003416128351359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.848 × 10⁹⁵(96-digit number)

28481046747605188597…18181003416128351361

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

5.696 × 10⁹⁵(96-digit number)

56962093495210377194…36362006832256702719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.696 × 10⁹⁵(96-digit number)

56962093495210377194…36362006832256702721

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

1.139 × 10⁹⁶(97-digit number)

11392418699042075438…72724013664513405439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.139 × 10⁹⁶(97-digit number)

11392418699042075438…72724013664513405441

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

2.278 × 10⁹⁶(97-digit number)

22784837398084150877…45448027329026810879

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 #2,752,291

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