Block #447,244

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/17/2014, 4:06:34 AM · Difficulty 10.3542 · 6,359,024 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b51118ed97c12787a7ec79c1ac867d479245c4a6a9848da13e3ce0d57eefef36

View on Chainz ↗

Height

#447,244

Difficulty

10.354248

Transactions

Size

1.27 KB

Version

Bits

0a5ab001

Nonce

27,857,093

Timestamp

3/17/2014, 4:06:34 AM

Confirmations

6,359,024

Mined by

⛏️ P2SHAZ9FhWGpmXYgNMoFW5NAihVY5jkerMhzTJ

Merkle Root

bbc640f82611b3d60a9de3f5ed98499907df75c7d300e89083fe076d6cd5510c

Transactions (3)

Coinbase448df68c1b6f31…02a7d24de3cc6b

1 in → 1 out9.3300 XPM109 B

AZ9FhWGp…kerMhzTJ

31961de6d89139…a5057039943cd0

4 in → 12 out37.3300 XPM876 B

AVE94w5J…WN4TXnY3 AWn9rWeZ…sxk6DT9k ALG6Kwki…JVRCDqef AdipcxVo…qAZrfiDs AcADmAoe…8iNnoMzB

5893183ba542da…410c684e964e43

1 in → 2 out7.2370 XPM226 B

ALhmUHSn…W6Lzmf2g AVwrYWvE…fDpRvNDy

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.

2.539 × 10⁹⁷(98-digit number)

25397702203961593109…24441806145501798399

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

2.539 × 10⁹⁷(98-digit number)

25397702203961593109…24441806145501798399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.539 × 10⁹⁷(98-digit number)

25397702203961593109…24441806145501798401

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

5.079 × 10⁹⁷(98-digit number)

50795404407923186218…48883612291003596799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.079 × 10⁹⁷(98-digit number)

50795404407923186218…48883612291003596801

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

1.015 × 10⁹⁸(99-digit number)

10159080881584637243…97767224582007193599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.015 × 10⁹⁸(99-digit number)

10159080881584637243…97767224582007193601

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

2.031 × 10⁹⁸(99-digit number)

20318161763169274487…95534449164014387199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.031 × 10⁹⁸(99-digit number)

20318161763169274487…95534449164014387201

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

4.063 × 10⁹⁸(99-digit number)

40636323526338548975…91068898328028774399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.063 × 10⁹⁸(99-digit number)

40636323526338548975…91068898328028774401

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 #447,244

Cookie Preferences