Block #402,164

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/13/2014, 6:57:40 AM · Difficulty 10.4316 · 6,399,323 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8157e9a1a67006c8e6ee34abadb74a662a3fef9f34a2d192093dea8a140d43bb

View on Chainz ↗

Height

#402,164

Difficulty

10.431648

Transactions

Size

6.05 KB

Version

Bits

0a6e807f

Nonce

190,390

Timestamp

2/13/2014, 6:57:40 AM

Confirmations

6,399,323

Mined by

AYRvXuTr13MD4FS87pKR469j8hCkbwFeLY

Merkle Root

8a2cb61548108b90504f6e954a7cbe9f6a13fe9dcf3ba299116de9afcf50be5b

Transactions (2)

Coinbase920e67fcb95ef9…05f795ac5fe925

1 in → 24 out9.2479 XPM879 B

AYRvXuTr…CkbwFeLY AW2fas42…gGAHYdHj AcgDwGo8…BBFwbjVo AU9n4fVh…kUqmhbCv AUDD9tmA…gJPQLnsz

a6f25f96ba2d75…c5b896c542c442

35 in → 1 out10.0000 XPM5.10 KB

AGBXiVcn…NRKq7Pbv

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.

1.422 × 10⁹⁶(97-digit number)

14226516309934591237…46159699965659310079

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

1.422 × 10⁹⁶(97-digit number)

14226516309934591237…46159699965659310079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.422 × 10⁹⁶(97-digit number)

14226516309934591237…46159699965659310081

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

2.845 × 10⁹⁶(97-digit number)

28453032619869182474…92319399931318620159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.845 × 10⁹⁶(97-digit number)

28453032619869182474…92319399931318620161

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

5.690 × 10⁹⁶(97-digit number)

56906065239738364948…84638799862637240319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.690 × 10⁹⁶(97-digit number)

56906065239738364948…84638799862637240321

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

1.138 × 10⁹⁷(98-digit number)

11381213047947672989…69277599725274480639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.138 × 10⁹⁷(98-digit number)

11381213047947672989…69277599725274480641

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

2.276 × 10⁹⁷(98-digit number)

22762426095895345979…38555199450548961279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.276 × 10⁹⁷(98-digit number)

22762426095895345979…38555199450548961281

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