Block #2,281,870

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/4/2017, 9:10:24 AM · Difficulty 10.9555 · 4,558,179 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

63da8a83cc498b62cb05f6a292456ae12882f70e3d2f2947c833613646f2fd02

View on Chainz ↗

Height

#2,281,870

Difficulty

10.955533

Transactions

Size

1.33 KB

Version

Bits

0af49dd7

Nonce

297,323,683

Timestamp

9/4/2017, 9:10:24 AM

Confirmations

4,558,179

Mined by

⛏️ P2SHAPFQyVZyZiMKFhqYTQpQoe6Q9YDrXibegd

Merkle Root

44bca48b570827801e847f943a8e6007132a5f8123641f3bd8e326bda71ebbe5

Transactions (5)

Coinbaseaea6d4c47d9112…171de7d0cee79e

1 in → 1 out8.3600 XPM109 B

APFQyVZy…DrXibegd

56765a450646b4…0b1b21a87ff656

2 in → 2 out15.4540 XPM340 B

AWddcU83…RSBKXbX6 AXjAuf16…DcE52q2K

32b9e0978d3f5f…045ffd0b3e714c

1 in → 2 out5.6327 XPM226 B

AMCrH8cv…xVgXxGxN AYUY6QBZ…nstBEWCQ

3ebf31e2d2ce70…41c72ae8e2586b

1 in → 2 out4.2420 XPM227 B

AHkz5YAt…DZ2yp9D5 AXCz3i15…bd3tZodd

1064766ccb64b3…e4e747f175612f

2 in → 2 out1.7231 XPM374 B

ARCFb9iC…HHVhgUv6 AQYCCBys…vasBnrUy

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.

3.733 × 10⁹⁵(96-digit number)

37333014439631738907…66742706706275235839

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

3.733 × 10⁹⁵(96-digit number)

37333014439631738907…66742706706275235839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.733 × 10⁹⁵(96-digit number)

37333014439631738907…66742706706275235841

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

7.466 × 10⁹⁵(96-digit number)

74666028879263477814…33485413412550471679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.466 × 10⁹⁵(96-digit number)

74666028879263477814…33485413412550471681

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

1.493 × 10⁹⁶(97-digit number)

14933205775852695562…66970826825100943359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.493 × 10⁹⁶(97-digit number)

14933205775852695562…66970826825100943361

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

2.986 × 10⁹⁶(97-digit number)

29866411551705391125…33941653650201886719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.986 × 10⁹⁶(97-digit number)

29866411551705391125…33941653650201886721

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

5.973 × 10⁹⁶(97-digit number)

59732823103410782251…67883307300403773439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.973 × 10⁹⁶(97-digit number)

59732823103410782251…67883307300403773441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #2,281,870

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