Block #2,643,656

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/2/2018, 4:45:24 AM · Difficulty 11.6894 · 4,186,866 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

60c2f31564a75b4ec93e5080f4d94b380f25f5ee1886f5b3efd9b1b2b46e2533

View on Chainz ↗

Height

#2,643,656

Difficulty

11.689428

Transactions

Size

2.26 KB

Version

Bits

0bb07e55

Nonce

520,347,278

Timestamp

5/2/2018, 4:45:24 AM

Confirmations

4,186,866

Mined by

⛏️ P2SHAJoewe1sYkX2cV5DvCTcvmwy3ETnRnAUru

Merkle Root

68343583511a90ae3c7d54f93ec15123070d0ee503fac3666cd9120504f688d4

Transactions (4)

Coinbase874fa7ab67bb52…1088919aedad8c

1 in → 1 out7.3500 XPM110 B

AJoewe1s…TnRnAUru

5e3a2c233a3146…0bf5c4161fddcc

4 in → 2 out33.5071 XPM667 B

ANhirdoK…8WctRPEt Aex6HLZj…Pzh97Civ

6fa490503ba067…faf7094cea21a1

8 in → 2 out20.0986 XPM1.23 KB

AbDYP3nU…n3vaA6c9 ARsiPW1r…oR9DimrE

7b4364c5cbcdff…3cc4d5aed32c9b

1 in → 1 out7.4391 XPM191 B

APE1MwnQ…JUvpLg9M

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.

8.217 × 10⁹⁶(97-digit number)

82171769743124271680…26045519422048174079

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

8.217 × 10⁹⁶(97-digit number)

82171769743124271680…26045519422048174079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.217 × 10⁹⁶(97-digit number)

82171769743124271680…26045519422048174081

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

1.643 × 10⁹⁷(98-digit number)

16434353948624854336…52091038844096348159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.643 × 10⁹⁷(98-digit number)

16434353948624854336…52091038844096348161

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

3.286 × 10⁹⁷(98-digit number)

32868707897249708672…04182077688192696319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.286 × 10⁹⁷(98-digit number)

32868707897249708672…04182077688192696321

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

6.573 × 10⁹⁷(98-digit number)

65737415794499417344…08364155376385392639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.573 × 10⁹⁷(98-digit number)

65737415794499417344…08364155376385392641

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

1.314 × 10⁹⁸(99-digit number)

13147483158899883468…16728310752770785279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.314 × 10⁹⁸(99-digit number)

13147483158899883468…16728310752770785281

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

2.629 × 10⁹⁸(99-digit number)

26294966317799766937…33456621505541570559

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 #2,643,656

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