Block #2,736,613

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/6/2018, 2:12:44 PM · Difficulty 11.6091 · 4,105,912 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d7223ac4582c7b861810a2855bcd8c29fff607d27053ff4013f16695a329f282

View on Chainz ↗

Height

#2,736,613

Difficulty

11.609102

Transactions

Size

2.02 KB

Version

Bits

0b9bee18

Nonce

79,328,499

Timestamp

7/6/2018, 2:12:44 PM

Confirmations

4,105,912

Mined by

⛏️ P2SHAHbLqbCxKB4qZqehikXirpH3jzaXFhrEEh

Merkle Root

8432ce1764b89d7be6ed465af0cd6a7cfbec9155eee3a6bae54c2033759efd14

Transactions (5)

Coinbasee90078d1d7864a…87dcd97be0bbaf

1 in → 1 out7.4600 XPM110 B

AHbLqbCx…aXFhrEEh

2aea8e18fbb7ca…546016f62d391d

7 in → 2 out20.0345 XPM1.02 KB

AWddcU83…RSBKXbX6 AT8KDaBM…ntcX4795

0baffb6990355e…f14839cb26b125

1 in → 2 out6.3379 XPM227 B

AaJCF4zr…DQ7WcHQP ANxNfXmZ…4p5PaHCM

56a56a1cb71627…b8b9f380c9104e

1 in → 2 out2.2482 XPM225 B

AGbm9W17…Jvw6eg2t AL9tdZsb…7qspPtrk

f6fa24dfa765e3…dd3faf2ccd8f91

2 in → 2 out5.8158 XPM373 B

AXzSvx5H…XuBaZeeK AKuViC7e…PZicCq8m

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.

2.353 × 10⁹⁸(99-digit number)

23530936828187279065…11384057419074109439

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

2.353 × 10⁹⁸(99-digit number)

23530936828187279065…11384057419074109439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.353 × 10⁹⁸(99-digit number)

23530936828187279065…11384057419074109441

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

4.706 × 10⁹⁸(99-digit number)

47061873656374558130…22768114838148218879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.706 × 10⁹⁸(99-digit number)

47061873656374558130…22768114838148218881

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

9.412 × 10⁹⁸(99-digit number)

94123747312749116261…45536229676296437759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.412 × 10⁹⁸(99-digit number)

94123747312749116261…45536229676296437761

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

1.882 × 10⁹⁹(100-digit number)

18824749462549823252…91072459352592875519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.882 × 10⁹⁹(100-digit number)

18824749462549823252…91072459352592875521

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

3.764 × 10⁹⁹(100-digit number)

37649498925099646504…82144918705185751039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.764 × 10⁹⁹(100-digit number)

37649498925099646504…82144918705185751041

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

7.529 × 10⁹⁹(100-digit number)

75298997850199293009…64289837410371502079

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 #2,736,613

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