Block #353,157

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/10/2014, 6:37:33 PM · Difficulty 10.3218 · 6,450,622 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f317eab89da7af40c7012331c02ed81bab600fd9e80e89c10e92784b4e989cb9

View on Chainz ↗

Height

#353,157

Difficulty

10.321831

Transactions

Size

1.01 KB

Version

Bits

0a526381

Nonce

78,985

Timestamp

1/10/2014, 6:37:33 PM

Confirmations

6,450,622

Mined by

⛏️ caR=Aac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

84a0ec55466e97ff652c681f61545bb5f3564a42470ac64cab57066d2c52ad76

Transactions (1)

Coinbase84a0ec55466e97…57066d2c52ad76

1 in → 26 out9.3700 XPM947 B

Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AZV4TwxQ…8JnQqSoH Ad9pSzHt…cpJ3y2zz AMiJebLB…rK2iN8iS

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.

3.192 × 10⁹⁸(99-digit number)

31921310375857467728…72118242181736466559

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

3.192 × 10⁹⁸(99-digit number)

31921310375857467728…72118242181736466559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.192 × 10⁹⁸(99-digit number)

31921310375857467728…72118242181736466561

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

6.384 × 10⁹⁸(99-digit number)

63842620751714935457…44236484363472933119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.384 × 10⁹⁸(99-digit number)

63842620751714935457…44236484363472933121

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

1.276 × 10⁹⁹(100-digit number)

12768524150342987091…88472968726945866239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.276 × 10⁹⁹(100-digit number)

12768524150342987091…88472968726945866241

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

2.553 × 10⁹⁹(100-digit number)

25537048300685974183…76945937453891732479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.553 × 10⁹⁹(100-digit number)

25537048300685974183…76945937453891732481

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

5.107 × 10⁹⁹(100-digit number)

51074096601371948366…53891874907783464959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.107 × 10⁹⁹(100-digit number)

51074096601371948366…53891874907783464961

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