Block #468,642

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/31/2014, 3:39:00 PM · Difficulty 10.4326 · 6,349,362 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

88449e707797cf2defdd97f673a9ab63f9341ebf05068952ced0847967939641

View on Chainz ↗

Height

#468,642

Difficulty

10.432633

Transactions

Size

2.24 KB

Version

Bits

0a6ec106

Nonce

8,550

Timestamp

3/31/2014, 3:39:00 PM

Confirmations

6,349,362

Mined by

⛏️ &aS9EAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

8ab138fdca371858897e48b9d8141c904b056c624ecd134b7d6d03fd77b240aa

Transactions (4)

Coinbase8fc547e99bfca8…04e668406140cd

1 in → 24 out9.1700 XPM879 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AQ8QAT3J…rCFKuVbR AScAzqGc…BZ6tV1vJ ATKK7iFz…wZm46KN1

aa0d263d8267bd…a925cbd443a782

3 in → 2 out27.7100 XPM420 B

ANTFivtu…tohTExFd AM7yc4iv…DbScvvJE

fb63023c3502a5…b261c235fc405e

2 in → 2 out18.3600 XPM305 B

ANTFivtu…tohTExFd AUuN41bE…UggXcVZn

3277fc5045b872…a1800c76dd59e3

4 in → 2 out19.3266 XPM601 B

ANTFivtu…tohTExFd APrMmEPv…dRgA9p6f

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.

1.655 × 10⁹⁸(99-digit number)

16552824237899015523…45560001387945303039

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

1.655 × 10⁹⁸(99-digit number)

16552824237899015523…45560001387945303039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.655 × 10⁹⁸(99-digit number)

16552824237899015523…45560001387945303041

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

3.310 × 10⁹⁸(99-digit number)

33105648475798031046…91120002775890606079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.310 × 10⁹⁸(99-digit number)

33105648475798031046…91120002775890606081

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

6.621 × 10⁹⁸(99-digit number)

66211296951596062093…82240005551781212159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.621 × 10⁹⁸(99-digit number)

66211296951596062093…82240005551781212161

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

1.324 × 10⁹⁹(100-digit number)

13242259390319212418…64480011103562424319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.324 × 10⁹⁹(100-digit number)

13242259390319212418…64480011103562424321

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

2.648 × 10⁹⁹(100-digit number)

26484518780638424837…28960022207124848639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.648 × 10⁹⁹(100-digit number)

26484518780638424837…28960022207124848641

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 #468,642

Cookie Preferences