Block #2,140,258

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/1/2017, 8:49:58 AM · Difficulty 10.8762 · 4,702,126 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

316a83f9d3266185fe25cc6060c6596fdd967d8a27617e233c805d6c04713e0b

View on Chainz ↗

Height

#2,140,258

Difficulty

10.876232

Transactions

Size

1.88 KB

Version

Bits

0ae050c3

Nonce

143,716,947

Timestamp

6/1/2017, 8:49:58 AM

Confirmations

4,702,126

Mined by

⛏️ P2SHAeuffqMNy8pKTUxyZic78LRd9uGEDpn7te

Merkle Root

cdbf7fb11688d47d1a11b1b5b8bcec37295337a9f0547ced35fcfb2d56d60395

Transactions (5)

Coinbased1a8e53dbc0f41…302072d4d3ac31

1 in → 1 out8.4800 XPM110 B

AeuffqMN…GEDpn7te

e30b5560f1235c…9e0d307d85bacc

3 in → 2 out1067.2500 XPM521 B

Aef2LHYA…dohTAM2y AbW8EmYq…k14E8on2

b70d8cffb26169…c815bfff60327a

3 in → 2 out232.7958 XPM522 B

AWfHSLDB…ULaupatc Ac286UJi…mUCLXAk7

c136583496dc1b…9693b160af339b

2 in → 2 out12.7663 XPM339 B

AdZ5hPR6…9We7AAeH AN83v1TU…kcXerDsJ

c0c6212e9bb83d…e6f43c12de3aa5

2 in → 2 out15.7379 XPM341 B

AHbyumek…ry7WXVsp AKZqGTXc…Mm32s2VS

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.

9.698 × 10⁹³(94-digit number)

96986101300016681290…33113554365057673679

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

9.698 × 10⁹³(94-digit number)

96986101300016681290…33113554365057673679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.698 × 10⁹³(94-digit number)

96986101300016681290…33113554365057673681

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

1.939 × 10⁹⁴(95-digit number)

19397220260003336258…66227108730115347359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.939 × 10⁹⁴(95-digit number)

19397220260003336258…66227108730115347361

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

3.879 × 10⁹⁴(95-digit number)

38794440520006672516…32454217460230694719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.879 × 10⁹⁴(95-digit number)

38794440520006672516…32454217460230694721

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

7.758 × 10⁹⁴(95-digit number)

77588881040013345032…64908434920461389439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.758 × 10⁹⁴(95-digit number)

77588881040013345032…64908434920461389441

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

1.551 × 10⁹⁵(96-digit number)

15517776208002669006…29816869840922778879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.551 × 10⁹⁵(96-digit number)

15517776208002669006…29816869840922778881

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 #2,140,258

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