Block #210,730

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/15/2013, 8:09:54 AM · Difficulty 9.9134 · 6,597,122 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

07a112071ddbed2cbcf128100f6222b0b9a8325445d45c9adbf5a6e235abfc67

View on Chainz ↗

Height

#210,730

Difficulty

9.913352

Transactions

Size

1.36 KB

Version

Bits

09e9d170

Nonce

40,979

Timestamp

10/15/2013, 8:09:54 AM

Confirmations

6,597,122

Mined by

⛏️ P2SHAUBma4S5uySZMrn3ZFMcGzLaC1FQrLorT7

Merkle Root

0cdbcd51b2a83de87f54de42dacb4be5c02f63126fd637449fe981bf78ee0a73

Transactions (3)

Coinbase4d6374506fb15a…b5dc6277e4d112

1 in → 1 out10.1800 XPM109 B

AUBma4S5…FQrLorT7

8e4c3ffda001ad…457674b2bbfc61

6 in → 2 out59.8091 XPM965 B

AcwhvqL3…iFhhrLTY ANP3mT5K…dkjrtVpK

cb7caced17a145…fb0839f6ed78eb

1 in → 2 out5.0852 XPM226 B

AVYA5FSq…eeZm8KGY AaHLNiUL…ejTLJTxh

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.

1.088 × 10⁹²(93-digit number)

10881858850716355759…60439659442906915839

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

1.088 × 10⁹²(93-digit number)

10881858850716355759…60439659442906915839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.088 × 10⁹²(93-digit number)

10881858850716355759…60439659442906915841

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

2.176 × 10⁹²(93-digit number)

21763717701432711519…20879318885813831679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.176 × 10⁹²(93-digit number)

21763717701432711519…20879318885813831681

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

4.352 × 10⁹²(93-digit number)

43527435402865423038…41758637771627663359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.352 × 10⁹²(93-digit number)

43527435402865423038…41758637771627663361

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

8.705 × 10⁹²(93-digit number)

87054870805730846077…83517275543255326719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.705 × 10⁹²(93-digit number)

87054870805730846077…83517275543255326721

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

1.741 × 10⁹³(94-digit number)

17410974161146169215…67034551086510653439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #210,730

Cookie Preferences