Block #2,213,059

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/19/2017, 6:26:27 AM · Difficulty 10.9439 · 4,618,693 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fcd4bbcca04ed7339c178a44b823b150dd5777934e69ea03f0103c3371974e5d

View on Chainz ↗

Height

#2,213,059

Difficulty

10.943887

Transactions

Size

9.93 KB

Version

Bits

0af1a290

Nonce

707,897,893

Timestamp

7/19/2017, 6:26:27 AM

Confirmations

4,618,693

Mined by

⛏️ P2SHANBgNogttmqxP3FKZSfinDMPcNBAR5KEHx

Merkle Root

e3ef946a27182ffba1d16e6f3e9db5e8ebba304728e1657226b479ed1a3a1e4d

Transactions (5)

Coinbasef3696c9a1f1d2a…39e7fa815ccb4c

1 in → 1 out8.4700 XPM110 B

ANBgNogt…BAR5KEHx

e69b99b4253074…b9251e15ac3c1f

3 in → 3 out6277.9742 XPM557 B

AcxhUhX6…N8N8w2tm AHicdPQX…H9Cxe2Ss AaS9eT5h…tyNr8Umc

5c06ac8168dada…f7d959b3e3000e

1 in → 2 out71398.0050 XPM227 B

AeZ8RZd4…VCjiNSsB ALm5Vh7M…iWjzJNtJ

04ed7e7e94e56e…19dcfb1b5ceeb2

5 in → 2 out61.1341 XPM817 B

AFpHJhDK…hyA1PvSQ ANaD5cjA…6ygNtqxb

a624cdc2a69e2d…ca252d9b3a82d6

56 in → 2 out297.2201 XPM8.17 KB

AammHJuN…yaRcHuV7 AVQLk9B3…bDkMQM9p

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.

5.948 × 10⁹⁷(98-digit number)

59480576436398829096…33111021073375805439

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

5.948 × 10⁹⁷(98-digit number)

59480576436398829096…33111021073375805439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.948 × 10⁹⁷(98-digit number)

59480576436398829096…33111021073375805441

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

1.189 × 10⁹⁸(99-digit number)

11896115287279765819…66222042146751610879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.189 × 10⁹⁸(99-digit number)

11896115287279765819…66222042146751610881

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

2.379 × 10⁹⁸(99-digit number)

23792230574559531638…32444084293503221759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.379 × 10⁹⁸(99-digit number)

23792230574559531638…32444084293503221761

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

4.758 × 10⁹⁸(99-digit number)

47584461149119063277…64888168587006443519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.758 × 10⁹⁸(99-digit number)

47584461149119063277…64888168587006443521

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

9.516 × 10⁹⁸(99-digit number)

95168922298238126554…29776337174012887039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.516 × 10⁹⁸(99-digit number)

95168922298238126554…29776337174012887041

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 #2,213,059

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