Block #2,633,799

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2018, 2:59:06 PM · Difficulty 11.2086 · 4,196,723 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

595ec6df3881d2ceb431f40d9eb9c54fc9015c7e04f7dbc376fe562d54f96d86

View on Chainz ↗

Height

#2,633,799

Difficulty

11.208597

Transactions

Size

1.09 KB

Version

Bits

0b3566a4

Nonce

43,323,803

Timestamp

4/28/2018, 2:59:06 PM

Confirmations

4,196,723

Mined by

⛏️ P2SHAZ2pQ1KARWnrfjL1fedgJkQ4FycvWfzjPd

Merkle Root

f1bd0481dac6141d2ba608017040f2dc685c04fadeed05d891a31bbc3d71fcb0

Transactions (2)

Coinbaseb4dfb1783fbb4b…16d9440bea4e95

1 in → 1 out7.9600 XPM110 B

AZ2pQ1KA…cvWfzjPd

b84033324d971d…74ae0529ceca7c

5 in → 5 out377.5453 XPM921 B

AKg5sJMp…WaVCTNNt ARznVePF…S7wvbB9s ASk9H3sY…qUG8r1d4 ALd65iyx…WC2oooUw AdwowGnz…JAYXijzB

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.

2.027 × 10⁹⁴(95-digit number)

20271221587478210817…64443550745618193319

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

2.027 × 10⁹⁴(95-digit number)

20271221587478210817…64443550745618193319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.027 × 10⁹⁴(95-digit number)

20271221587478210817…64443550745618193321

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

4.054 × 10⁹⁴(95-digit number)

40542443174956421635…28887101491236386639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.054 × 10⁹⁴(95-digit number)

40542443174956421635…28887101491236386641

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

8.108 × 10⁹⁴(95-digit number)

81084886349912843271…57774202982472773279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.108 × 10⁹⁴(95-digit number)

81084886349912843271…57774202982472773281

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

1.621 × 10⁹⁵(96-digit number)

16216977269982568654…15548405964945546559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.621 × 10⁹⁵(96-digit number)

16216977269982568654…15548405964945546561

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

3.243 × 10⁹⁵(96-digit number)

32433954539965137308…31096811929891093119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.243 × 10⁹⁵(96-digit number)

32433954539965137308…31096811929891093121

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

6.486 × 10⁹⁵(96-digit number)

64867909079930274617…62193623859782186239

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 #2,633,799

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