Block #2,134,108

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/27/2017, 12:29:25 AM · Difficulty 10.9089 · 4,708,247 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b7927b309f1b0553dae8e2e207a4b0fbbbbc24523680fae27ea1181da58321aa

View on Chainz ↗

Height

#2,134,108

Difficulty

10.908854

Transactions

Size

1.87 KB

Version

Bits

0ae8aaa6

Nonce

25,757,006

Timestamp

5/27/2017, 12:29:25 AM

Confirmations

4,708,247

Mined by

⛏️ P2SHAcNvAUDTqdV7qkEKfY2RfjQ4fPgEMh4h38

Merkle Root

550076ffe329736b2a9c4db6493cd6ff68be24507194e29f626ec77728d8446c

Transactions (4)

Coinbase5f228feeb8d032…b24d6a4e09afc7

1 in → 1 out8.4300 XPM110 B

AcNvAUDT…gEMh4h38

1af1ad9b998cb0…77dceceb031809

1 in → 2 out109833.3614 XPM226 B

AWSpM1vT…ukZRfqjD ActHiDvW…rbVbi2gb

6fe556704e6a50…2f5958f363aeba

8 in → 2 out1226.3842 XPM1.23 KB

AbiJKggY…HChYUbQ3 AZAUi21T…4Mwjwt9m

2dfcf58afe94a4…59830d01f49011

1 in → 2 out109391.5105 XPM227 B

AbbdX2ib…ZU98LWf6 AG2x6KTL…RfJpdTvv

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.

2.590 × 10⁹⁷(98-digit number)

25907469431074010737…19958579249487319039

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

2.590 × 10⁹⁷(98-digit number)

25907469431074010737…19958579249487319039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.590 × 10⁹⁷(98-digit number)

25907469431074010737…19958579249487319041

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

5.181 × 10⁹⁷(98-digit number)

51814938862148021474…39917158498974638079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.181 × 10⁹⁷(98-digit number)

51814938862148021474…39917158498974638081

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

1.036 × 10⁹⁸(99-digit number)

10362987772429604294…79834316997949276159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.036 × 10⁹⁸(99-digit number)

10362987772429604294…79834316997949276161

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

2.072 × 10⁹⁸(99-digit number)

20725975544859208589…59668633995898552319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.072 × 10⁹⁸(99-digit number)

20725975544859208589…59668633995898552321

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

4.145 × 10⁹⁸(99-digit number)

41451951089718417179…19337267991797104639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.145 × 10⁹⁸(99-digit number)

41451951089718417179…19337267991797104641

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 #2,134,108

Cookie Preferences