Block #422,147

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/27/2014, 12:37:19 PM · Difficulty 10.3800 · 6,385,789 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

824e2d5e2c579ebc60d5bc6bc6c3155bd9c8d44158cb4845b27abbbfee347319

View on Chainz ↗

Height

#422,147

Difficulty

10.380044

Transactions

Size

5.54 KB

Version

Bits

0a614a96

Nonce

489,251

Timestamp

2/27/2014, 12:37:19 PM

Confirmations

6,385,789

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

074b8d2027eab48bd5b36f338c8596f5cb703c48028bd630b83d563e9dba8aca

Transactions (3)

Coinbasedaf100ac769674…8d938f78b77ae0

1 in → 1 out9.3300 XPM110 B

AeKNrjNj…1NEq95Ta

f88f3e0d5323c4…e5f18263476d9b

3 in → 9 out27.8000 XPM657 B

ANU8S1BR…65yNoREy Acn35Cbn…kDx6QvGN Aepeftrx…HLuGLNLy AHCuz9P2…41tUcRdy ANQKf2g4…29NaVj23

84b06cb349861a…567171ea1f47ac

32 in → 2 out9.4779 XPM4.70 KB

AHCMQpxd…bSYjqzJP AVFSC1ke…e2TB6Q3u

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.

9.736 × 10⁹⁶(97-digit number)

97368637677745056990…30601413671769092799

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

9.736 × 10⁹⁶(97-digit number)

97368637677745056990…30601413671769092799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.736 × 10⁹⁶(97-digit number)

97368637677745056990…30601413671769092801

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

1.947 × 10⁹⁷(98-digit number)

19473727535549011398…61202827343538185599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.947 × 10⁹⁷(98-digit number)

19473727535549011398…61202827343538185601

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

3.894 × 10⁹⁷(98-digit number)

38947455071098022796…22405654687076371199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.894 × 10⁹⁷(98-digit number)

38947455071098022796…22405654687076371201

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

7.789 × 10⁹⁷(98-digit number)

77894910142196045592…44811309374152742399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.789 × 10⁹⁷(98-digit number)

77894910142196045592…44811309374152742401

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

1.557 × 10⁹⁸(99-digit number)

15578982028439209118…89622618748305484799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.557 × 10⁹⁸(99-digit number)

15578982028439209118…89622618748305484801

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 #422,147

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