Block #214,564

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/17/2013, 1:49:27 PM · Difficulty 9.9235 · 6,588,086 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d339c127d364b0148a6be2081c640ad371c3e679a0161182969a5f2b4c2eadcf

View on Chainz ↗

Height

#214,564

Difficulty

9.923479

Transactions

Size

357 B

Version

Bits

09ec6923

Nonce

117,026

Timestamp

10/17/2013, 1:49:27 PM

Confirmations

6,588,086

Mined by

⛏️ P2SHAHPLSWVdVVmfZ1Mw8oxTBdXzN3ZdicvSUu

Merkle Root

8a4cec410af77f53a03dc9b01fbb7e5ba9f3f8ba9652fb6bbc39cb34e45c6352

Transactions (2)

Coinbasea7c04755785f1c…5b5320d7acc852

1 in → 1 out10.1500 XPM109 B

AHPLSWVd…ZdicvSUu

eeb2c9726962b4…ca0d8e571f27bd

1 in → 1 out10.1900 XPM159 B

AaiQ25kC…uarGkYVE

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.

3.269 × 10⁹²(93-digit number)

32691520376868840258…05901399157239942719

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

3.269 × 10⁹²(93-digit number)

32691520376868840258…05901399157239942719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.269 × 10⁹²(93-digit number)

32691520376868840258…05901399157239942721

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

6.538 × 10⁹²(93-digit number)

65383040753737680517…11802798314479885439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.538 × 10⁹²(93-digit number)

65383040753737680517…11802798314479885441

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

1.307 × 10⁹³(94-digit number)

13076608150747536103…23605596628959770879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.307 × 10⁹³(94-digit number)

13076608150747536103…23605596628959770881

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

2.615 × 10⁹³(94-digit number)

26153216301495072207…47211193257919541759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.615 × 10⁹³(94-digit number)

26153216301495072207…47211193257919541761

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

5.230 × 10⁹³(94-digit number)

52306432602990144414…94422386515839083519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.230 × 10⁹³(94-digit number)

52306432602990144414…94422386515839083521

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