Block #2,058,002

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/6/2017, 3:24:29 AM · Difficulty 10.8365 · 4,779,780 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8a447e944e48cfb4e0e3ccf1721d76211ea2471a1615d2b2d493aa5d7d182cb7

View on Chainz ↗

Height

#2,058,002

Difficulty

10.836493

Transactions

Size

389 B

Version

Bits

0ad62461

Nonce

857,149,721

Timestamp

4/6/2017, 3:24:29 AM

Confirmations

4,779,780

Mined by

⛏️ P2SHAQrCeggzS38kq87PYt7iaSnEe4zcD5CdKE

Merkle Root

a08eff7fda07088046505509095448de149c572e9ded27663a923de589870515

Transactions (2)

Coinbaseaa4ee7b9c6eba1…d7864576e1aa98

1 in → 1 out8.5100 XPM109 B

AQrCeggz…zcD5CdKE

027adddfb09f66…a56b761623ad64

1 in → 1 out0.1153 XPM191 B

ATqEnDUY…FcfWBKqc

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.

1.293 × 10⁹²(93-digit number)

12933593892017333806…18464420988937909859

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

1.293 × 10⁹²(93-digit number)

12933593892017333806…18464420988937909859

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.293 × 10⁹²(93-digit number)

12933593892017333806…18464420988937909861

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

2.586 × 10⁹²(93-digit number)

25867187784034667613…36928841977875819719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.586 × 10⁹²(93-digit number)

25867187784034667613…36928841977875819721

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

5.173 × 10⁹²(93-digit number)

51734375568069335227…73857683955751639439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.173 × 10⁹²(93-digit number)

51734375568069335227…73857683955751639441

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

1.034 × 10⁹³(94-digit number)

10346875113613867045…47715367911503278879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.034 × 10⁹³(94-digit number)

10346875113613867045…47715367911503278881

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

2.069 × 10⁹³(94-digit number)

20693750227227734090…95430735823006557759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.069 × 10⁹³(94-digit number)

20693750227227734090…95430735823006557761

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 #2,058,002

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