Block #2,646,831

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/3/2018, 1:48:12 PM · Difficulty 11.7549 · 4,198,426 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

79d0c31b244ab517f6308502051403cb929880e791a8ed1c88110a593ccb35c3

View on Chainz ↗

Height

#2,646,831

Difficulty

11.754933

Transactions

Size

426 B

Version

Bits

0bc14347

Nonce

175,129,874

Timestamp

5/3/2018, 1:48:12 PM

Confirmations

4,198,426

Mined by

⛏️ P2SHAanYHYCEpwrnYaYtJVtZ4n2SBAHEsakxH7

Merkle Root

e47afa16332973f42dfa4cdcc2c929a3985e84fde9b7c19c88f73868d5f03b80

Transactions (2)

Coinbase5834195e9893ae…a60f2bc50b7d16

1 in → 1 out7.2300 XPM110 B

AanYHYCE…HEsakxH7

1c62b90b159078…6bbbd8f54aefa0

1 in → 2 out149772.2551 XPM226 B

Aa4HLcBp…aGubpZNc AFnTfkSa…ZpVpqTx1

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.

4.518 × 10⁹⁵(96-digit number)

45184814551896413118…29696040798513242879

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

4.518 × 10⁹⁵(96-digit number)

45184814551896413118…29696040798513242879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.518 × 10⁹⁵(96-digit number)

45184814551896413118…29696040798513242881

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

9.036 × 10⁹⁵(96-digit number)

90369629103792826237…59392081597026485759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.036 × 10⁹⁵(96-digit number)

90369629103792826237…59392081597026485761

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

1.807 × 10⁹⁶(97-digit number)

18073925820758565247…18784163194052971519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.807 × 10⁹⁶(97-digit number)

18073925820758565247…18784163194052971521

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

3.614 × 10⁹⁶(97-digit number)

36147851641517130495…37568326388105943039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.614 × 10⁹⁶(97-digit number)

36147851641517130495…37568326388105943041

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

7.229 × 10⁹⁶(97-digit number)

72295703283034260990…75136652776211886079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.229 × 10⁹⁶(97-digit number)

72295703283034260990…75136652776211886081

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

1.445 × 10⁹⁷(98-digit number)

14459140656606852198…50273305552423772159

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 #2,646,831

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