Block #2,869,863

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/6/2018, 2:40:30 PM · Difficulty 11.6674 · 3,972,391 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8bf718f10e983270a2f72b2ab5fef3d6d17a19f5b0e216acf58000095fc0a633

View on Chainz ↗

Height

#2,869,863

Difficulty

11.667410

Transactions

Size

1.19 KB

Version

Bits

0baadb68

Nonce

518,059,843

Timestamp

10/6/2018, 2:40:30 PM

Confirmations

3,972,391

Mined by

⛏️ P2SHAMvEffAfUfqV9bJcEaytxjQCfNgJ7emvQy

Merkle Root

c81f1668a41f4af61664a51bfed5451516cb45a040e71a670a50fe739e195037

Transactions (4)

Coinbase3f815a4e54bee3…435f8f5b24d498

1 in → 1 out7.3600 XPM110 B

AMvEffAf…gJ7emvQy

c4d13dda7a7f8b…3e9cb433b39c46

2 in → 2 out14.6700 XPM307 B

AT9SDs5w…tYWZhzpF APVKWthF…PMMxwRoz

803f5910ac305f…739dfd4204621b

2 in → 2 out12.0600 XPM341 B

Aek7aQzY…4495YRvK ARC6G7Gz…XG8EBDaa

ce904ad44f1458…53dd7ded95f73b

2 in → 2 out5.0694 XPM375 B

AdGFnV3a…o6n2zX3x AanmKZ94…YLwCzrBh

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.

5.934 × 10⁹⁵(96-digit number)

59347321380011447656…91708174993849190079

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

5.934 × 10⁹⁵(96-digit number)

59347321380011447656…91708174993849190079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.934 × 10⁹⁵(96-digit number)

59347321380011447656…91708174993849190081

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

1.186 × 10⁹⁶(97-digit number)

11869464276002289531…83416349987698380159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.186 × 10⁹⁶(97-digit number)

11869464276002289531…83416349987698380161

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

2.373 × 10⁹⁶(97-digit number)

23738928552004579062…66832699975396760319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.373 × 10⁹⁶(97-digit number)

23738928552004579062…66832699975396760321

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

4.747 × 10⁹⁶(97-digit number)

47477857104009158125…33665399950793520639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.747 × 10⁹⁶(97-digit number)

47477857104009158125…33665399950793520641

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

9.495 × 10⁹⁶(97-digit number)

94955714208018316250…67330799901587041279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.495 × 10⁹⁶(97-digit number)

94955714208018316250…67330799901587041281

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

1.899 × 10⁹⁷(98-digit number)

18991142841603663250…34661599803174082559

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 #2,869,863

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