Block #439,456

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/11/2014, 5:07:03 PM · Difficulty 10.3590 · 6,364,323 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2f0f23f2159ffd3363cc5011b7c2b4e67650de5888ef570246f9c815565451be

View on Chainz ↗

Height

#439,456

Difficulty

10.358974

Transactions

Size

3.47 KB

Version

Bits

0a5be5bc

Nonce

12,601

Timestamp

3/11/2014, 5:07:03 PM

Confirmations

6,364,323

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

8fa92c1b2171f6ce918ae57bf5920039f4ebabc9fcd8b527d0111cd0a4863cc4

Transactions (4)

Coinbased7214ef9dd0405…b0a7fcd5a10a27

1 in → 19 out9.3441 XPM709 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AMW1p9oT…2TzdaZxH AUFKXvnz…342ApNcm ASgUri65…C7NLcyBg

45d7bf8cbfe827…4c8a1479a382e3

3 in → 1 out3.0000 XPM490 B

AKyvDdPe…xJDsp6Dc

9ea66d942f1f22…8d0875043ccd2c

2 in → 5 out12.6950 XPM442 B

AbfkiWwg…fhe7yhRU AHWcE641…mx64JLTa AeKNrjNj…1NEq95Ta AKpWfTgS…JDmAtbgJ AUdoR1CL…hGjJfPiM

063521c14c1941…03b03f02df4e56

12 in → 1 out4.0406 XPM1.77 KB

Ac8o5MFs…J2PmNB4S

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.

5.860 × 10⁹⁸(99-digit number)

58601204291489191731…75843009402942783999

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

5.860 × 10⁹⁸(99-digit number)

58601204291489191731…75843009402942783999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.860 × 10⁹⁸(99-digit number)

58601204291489191731…75843009402942784001

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

1.172 × 10⁹⁹(100-digit number)

11720240858297838346…51686018805885567999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.172 × 10⁹⁹(100-digit number)

11720240858297838346…51686018805885568001

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

2.344 × 10⁹⁹(100-digit number)

23440481716595676692…03372037611771135999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.344 × 10⁹⁹(100-digit number)

23440481716595676692…03372037611771136001

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

4.688 × 10⁹⁹(100-digit number)

46880963433191353385…06744075223542271999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.688 × 10⁹⁹(100-digit number)

46880963433191353385…06744075223542272001

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

9.376 × 10⁹⁹(100-digit number)

93761926866382706770…13488150447084543999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.376 × 10⁹⁹(100-digit number)

93761926866382706770…13488150447084544001

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