Block #347,670

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/7/2014, 8:38:15 AM · Difficulty 10.2403 · 6,454,840 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7d97d038ee74d1cc4b16282edfdf3282d0ff2e771128d994d70cf34e93771f83

View on Chainz ↗

Height

#347,670

Difficulty

10.240291

Transactions

Size

3.73 KB

Version

Bits

0a3d83b8

Nonce

211,790

Timestamp

1/7/2014, 8:38:15 AM

Confirmations

6,454,840

Mined by

⛏️ NaR7Aac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

17a3c7c3155a69c0e6678a94d34622383b2dfe15b6e43b0e66d490e424433f15

Transactions (4)

Coinbased98d06f2f4ea45…72dae9f3159f27

1 in → 22 out9.5200 XPM811 B

Aac9Hjdg…P4ktypc3 AUnkFe8H…fvenjA4X AZV4TwxQ…8JnQqSoH AP5UvYhU…vLTDwkdA AFutDVqJ…TJTJj6UF

305e5ebb4767b4…5e751997a63e16

12 in → 1 out87.1973 XPM1.78 KB

AYnVUMsi…4WtHuYAK

60ca784e3f1217…af2b07aac5d0c2

4 in → 13 out38.7131 XPM906 B

AdcduiYL…15jUwoD9 ALX3iX2q…1oQ8ea28 AQPKVZ3U…pFSRayvv ASTcaxJ4…gURy1LJz AKXDwiQX…ByKkCqrj

8fcee1079e915b…05535af136db0e

1 in → 1 out3.1587 XPM193 B

AMQkuN3B…nsEWBtft

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.

7.073 × 10⁹⁵(96-digit number)

70739634893698089763…93183227641477065439

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

7.073 × 10⁹⁵(96-digit number)

70739634893698089763…93183227641477065439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.073 × 10⁹⁵(96-digit number)

70739634893698089763…93183227641477065441

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

1.414 × 10⁹⁶(97-digit number)

14147926978739617952…86366455282954130879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.414 × 10⁹⁶(97-digit number)

14147926978739617952…86366455282954130881

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

2.829 × 10⁹⁶(97-digit number)

28295853957479235905…72732910565908261759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.829 × 10⁹⁶(97-digit number)

28295853957479235905…72732910565908261761

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

5.659 × 10⁹⁶(97-digit number)

56591707914958471810…45465821131816523519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.659 × 10⁹⁶(97-digit number)

56591707914958471810…45465821131816523521

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

1.131 × 10⁹⁷(98-digit number)

11318341582991694362…90931642263633047039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.131 × 10⁹⁷(98-digit number)

11318341582991694362…90931642263633047041

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