Block #212,079

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/16/2013, 1:53:13 AM · Difficulty 9.9182 · 6,592,236 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3a1978fc63b9124d72a723d3ac3c5542906c4e251449845b4e02543b1f313639

View on Chainz ↗

Height

#212,079

Difficulty

9.918193

Transactions

Size

1.37 KB

Version

Bits

09eb0eaf

Nonce

23,498

Timestamp

10/16/2013, 1:53:13 AM

Confirmations

6,592,236

Mined by

⛏️ P2SHANjoZavnakwYPiwayYapVGjExRVrcsapZU

Merkle Root

f94519df052c2012fa016b491210df6af4ba2d4bcad540d61eac69db64b382ec

Transactions (5)

Coinbaseb15a9e2fa56b4b…3e67f27f23071d

1 in → 1 out10.1900 XPM109 B

ANjoZavn…VrcsapZU

8a6608a88670c3…14be0439b00695

3 in → 2 out2315.0100 XPM522 B

AHPXiLSk…rni3kjh5 ALtckAK7…S8RkrR2D

54792af783e10c…e425589616dbec

1 in → 2 out0.7300 XPM226 B

AdBcJVg3…tNGzwJfW ATZB28TS…D1zSDA64

2160fa82b76ea2…37fcedb5e285bd

1 in → 2 out0.8700 XPM227 B

ANN52XZo…XBfpRB3A AJiLoewR…DW22m9Z6

2acad8e9121d61…102d59bf9f2a9a

1 in → 2 out0.3700 XPM226 B

AZtnJhZX…ug7wd1US ANN52XZo…XBfpRB3A

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.

6.629 × 10⁹¹(92-digit number)

66298695742633792162…70537741308092431999

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

6.629 × 10⁹¹(92-digit number)

66298695742633792162…70537741308092431999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.629 × 10⁹¹(92-digit number)

66298695742633792162…70537741308092432001

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

1.325 × 10⁹²(93-digit number)

13259739148526758432…41075482616184863999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.325 × 10⁹²(93-digit number)

13259739148526758432…41075482616184864001

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

2.651 × 10⁹²(93-digit number)

26519478297053516865…82150965232369727999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.651 × 10⁹²(93-digit number)

26519478297053516865…82150965232369728001

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

5.303 × 10⁹²(93-digit number)

53038956594107033730…64301930464739455999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.303 × 10⁹²(93-digit number)

53038956594107033730…64301930464739456001

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

1.060 × 10⁹³(94-digit number)

10607791318821406746…28603860929478911999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.060 × 10⁹³(94-digit number)

10607791318821406746…28603860929478912001

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