Block #2,760,695

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/22/2018, 9:02:39 PM · Difficulty 11.6559 · 4,057,243 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

950995bf4ff820c966b7c86ddb2d4cbcb74180d6a2d21a49e319b503252e72a4

View on Chainz ↗

Height

#2,760,695

Difficulty

11.655937

Transactions

Size

1.53 KB

Version

Bits

0ba7eb81

Nonce

547,967,260

Timestamp

7/22/2018, 9:02:39 PM

Confirmations

4,057,243

Mined by

⛏️ P2SHAJ3dwq97eYqM1DjhxkJrmY9kcK7v3tfTRR

Merkle Root

d8ba93563d3b63a8aefd67b96c4ee2ad4b5221fd5f852de3b578acec813d8c76

Transactions (4)

Coinbasee454175098e91e…46d3cc4e181345

1 in → 1 out7.3800 XPM109 B

AJ3dwq97…7v3tfTRR

4280d8299bc506…753dea8effb724

6 in → 2 out40.0836 XPM797 B

AKxyVgfv…3DbH8Mh9 AGQwBTXu…WJfDT46W

0233d0a49501fe…f03bd3e7804263

2 in → 2 out10.6308 XPM340 B

AHdKji7P…JwU9aygE AVvgHwJr…kj4Gjujc

1fee1bfc2e32de…207caffcaecc94

1 in → 2 out2.3075 XPM226 B

AavQ7qx5…scjQqMhd ARMFdT2w…TGxHik4a

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.

9.005 × 10⁹⁶(97-digit number)

90051815841101545625…28921554085688115199

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

9.005 × 10⁹⁶(97-digit number)

90051815841101545625…28921554085688115199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.005 × 10⁹⁶(97-digit number)

90051815841101545625…28921554085688115201

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

1.801 × 10⁹⁷(98-digit number)

18010363168220309125…57843108171376230399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.801 × 10⁹⁷(98-digit number)

18010363168220309125…57843108171376230401

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

3.602 × 10⁹⁷(98-digit number)

36020726336440618250…15686216342752460799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.602 × 10⁹⁷(98-digit number)

36020726336440618250…15686216342752460801

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

7.204 × 10⁹⁷(98-digit number)

72041452672881236500…31372432685504921599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.204 × 10⁹⁷(98-digit number)

72041452672881236500…31372432685504921601

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

1.440 × 10⁹⁸(99-digit number)

14408290534576247300…62744865371009843199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.440 × 10⁹⁸(99-digit number)

14408290534576247300…62744865371009843201

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

2.881 × 10⁹⁸(99-digit number)

28816581069152494600…25489730742019686399

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 #2,760,695

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