Block #2,641,899

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/1/2018, 12:50:15 PM · Difficulty 11.6358 · 4,199,785 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d84eab01b5c0552cb21b9aa5a5241c5de1486146aac4ec355b9a1e8cbf15a150

View on Chainz ↗

Height

#2,641,899

Difficulty

11.635783

Transactions

Size

720 B

Version

Bits

0ba2c2af

Nonce

319,253,932

Timestamp

5/1/2018, 12:50:15 PM

Confirmations

4,199,785

Mined by

⛏️ P2SHANd7KEUm2sU6ChZgof7eoX3R3GgWXhRkaB

Merkle Root

87005c5537b22aaaa51ab31c4bc2d2816177bc6ce1518852d744324ca3056ef5

Transactions (2)

Coinbaseb538b46a438916…f7eeb4c374bc36

1 in → 1 out7.3900 XPM110 B

ANd7KEUm…gWXhRkaB

7ec10a1814152a…960dc75e1e879e

3 in → 2 out9.4674 XPM521 B

AJsrgx7b…ggGpoV5j AdQUiDVS…Xdoy8WpY

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.

9.970 × 10⁹²(93-digit number)

99701388684718415272…80756880985124156159

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

9.970 × 10⁹²(93-digit number)

99701388684718415272…80756880985124156159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.970 × 10⁹²(93-digit number)

99701388684718415272…80756880985124156161

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

1.994 × 10⁹³(94-digit number)

19940277736943683054…61513761970248312319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.994 × 10⁹³(94-digit number)

19940277736943683054…61513761970248312321

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

3.988 × 10⁹³(94-digit number)

39880555473887366108…23027523940496624639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.988 × 10⁹³(94-digit number)

39880555473887366108…23027523940496624641

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

7.976 × 10⁹³(94-digit number)

79761110947774732217…46055047880993249279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.976 × 10⁹³(94-digit number)

79761110947774732217…46055047880993249281

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

1.595 × 10⁹⁴(95-digit number)

15952222189554946443…92110095761986498559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.595 × 10⁹⁴(95-digit number)

15952222189554946443…92110095761986498561

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

3.190 × 10⁹⁴(95-digit number)

31904444379109892887…84220191523972997119

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 #2,641,899

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