Block #314,700

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/16/2013, 3:00:42 AM · Difficulty 10.0705 · 6,502,770 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7f9f92dab7a0bde776252c88c038869f7a13216b50784e2c8361b74861372002

View on Chainz ↗

Height

#314,700

Difficulty

10.070532

Transactions

Size

1.67 KB

Version

Bits

0a120e62

Nonce

7,083

Timestamp

12/16/2013, 3:00:42 AM

Confirmations

6,502,770

Mined by

⛏️ LaRkAd9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

599e570be5b41ec2599c5f2bd9a2c12dfc5266c0d9873f613a46897c35d115e1

Transactions (4)

Coinbase417b0b480b87eb…2d546c02c6cc36

1 in → 26 out9.8500 XPM947 B

Ad9pSzHt…cpJ3y2zz Aac9Hjdg…P4ktypc3 AQM5Zq4c…Wu5TRqLn AWXYBWKP…qQAoisBJ ANf2u7gz…y2batLmq

056c5c80280c77…9ba9de2c73cd69

1 in → 2 out8.9615 XPM225 B

AFmwxKVY…RyAswLiR Acne5tW7…DJMFXrLZ

33b0fb1de441cb…659ba57a6a2116

1 in → 2 out8.9617 XPM226 B

AMjDpZ33…us7kH7MD ARxUP9U5…rDwwnVbw

84c11be23f88f5…e600f1dfb6f751

1 in → 2 out8.9598 XPM226 B

AU9u66X1…xm15jgXk AUSEvpgj…pEGkKLia

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.

6.426 × 10⁹²(93-digit number)

64268270521557127930…48462105456750679039

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

6.426 × 10⁹²(93-digit number)

64268270521557127930…48462105456750679039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.426 × 10⁹²(93-digit number)

64268270521557127930…48462105456750679041

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

1.285 × 10⁹³(94-digit number)

12853654104311425586…96924210913501358079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.285 × 10⁹³(94-digit number)

12853654104311425586…96924210913501358081

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

2.570 × 10⁹³(94-digit number)

25707308208622851172…93848421827002716159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.570 × 10⁹³(94-digit number)

25707308208622851172…93848421827002716161

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

5.141 × 10⁹³(94-digit number)

51414616417245702344…87696843654005432319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.141 × 10⁹³(94-digit number)

51414616417245702344…87696843654005432321

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

1.028 × 10⁹⁴(95-digit number)

10282923283449140468…75393687308010864639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.028 × 10⁹⁴(95-digit number)

10282923283449140468…75393687308010864641

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 #314,700

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