Block #2,117,588

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/15/2017, 3:11:16 PM · Difficulty 10.9061 · 4,723,244 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

784cdde809c6298d84db73574fa17db00b44fd19094e9f1a38ed849a2a3f5b2d

View on Chainz ↗

Height

#2,117,588

Difficulty

10.906060

Transactions

Size

945 B

Version

Bits

0ae7f38b

Nonce

1,971,967,465

Timestamp

5/15/2017, 3:11:16 PM

Confirmations

4,723,244

Mined by

⛏️ P2SHARHjRqQmvgxsEEPHFMSkDhxSGLKTPxM2QF

Merkle Root

771abda1b6437d456d4c92f2e06807253ab78466b412facd28d9424326ede3be

Transactions (3)

Coinbase53b887353de979…f1343f0318c673

1 in → 1 out8.4100 XPM110 B

ARHjRqQm…KTPxM2QF

8b14a0ee352328…913ffbf5ac7d35

3 in → 2 out1632.1424 XPM520 B

ARspTngk…C728MPTE AR8WCZQt…gUBCpZDo

121bff2030b22e…4de13e620ea4e3

1 in → 2 out66476.9334 XPM225 B

AdXyA6cW…PKymsVvm AaEkL9U2…HFNsh9fa

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.

3.210 × 10⁹⁴(95-digit number)

32102230918056498348…64671371797794325959

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

3.210 × 10⁹⁴(95-digit number)

32102230918056498348…64671371797794325959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.210 × 10⁹⁴(95-digit number)

32102230918056498348…64671371797794325961

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

6.420 × 10⁹⁴(95-digit number)

64204461836112996697…29342743595588651919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.420 × 10⁹⁴(95-digit number)

64204461836112996697…29342743595588651921

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

1.284 × 10⁹⁵(96-digit number)

12840892367222599339…58685487191177303839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.284 × 10⁹⁵(96-digit number)

12840892367222599339…58685487191177303841

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

2.568 × 10⁹⁵(96-digit number)

25681784734445198679…17370974382354607679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.568 × 10⁹⁵(96-digit number)

25681784734445198679…17370974382354607681

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

5.136 × 10⁹⁵(96-digit number)

51363569468890397358…34741948764709215359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.136 × 10⁹⁵(96-digit number)

51363569468890397358…34741948764709215361

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

1.027 × 10⁹⁶(97-digit number)

10272713893778079471…69483897529418430719

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 #2,117,588

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