Block #396,958

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/9/2014, 6:09:12 PM · Difficulty 10.4160 · 6,399,136 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

354702b4cf146043b6c073e06126889871690f7a84c3a8c5f7031e8514b6f3d7

View on Chainz ↗

Height

#396,958

Difficulty

10.415995

Transactions

Size

960 B

Version

Bits

0a6a7eae

Nonce

8,542

Timestamp

2/9/2014, 6:09:12 PM

Confirmations

6,399,136

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

6d1b799fdb4accb1b2ede4bd20f49a0841459ad01b6e0c316944352588e92d41

Transactions (3)

Coinbase42fbbe5a879985…8d0003fca42cb3

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

498b55876fbc15…4a8aacec5f890b

1 in → 2 out4.2737 XPM226 B

AGCgcWgr…cK9nFU3p AZXzmeNz…t2aAZx5B

e0460ff2b01ac3…d750691c1ca981

3 in → 2 out1.0938 XPM524 B

AeJ9GBaH…4ZUH8yvp AMAn2RqT…WgyLvxav

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.

1.759 × 10¹⁰³(104-digit number)

17596175848481708243…57700125693533224959

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

1.759 × 10¹⁰³(104-digit number)

17596175848481708243…57700125693533224959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.759 × 10¹⁰³(104-digit number)

17596175848481708243…57700125693533224961

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

3.519 × 10¹⁰³(104-digit number)

35192351696963416487…15400251387066449919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.519 × 10¹⁰³(104-digit number)

35192351696963416487…15400251387066449921

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

7.038 × 10¹⁰³(104-digit number)

70384703393926832974…30800502774132899839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.038 × 10¹⁰³(104-digit number)

70384703393926832974…30800502774132899841

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

1.407 × 10¹⁰⁴(105-digit number)

14076940678785366594…61601005548265799679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.407 × 10¹⁰⁴(105-digit number)

14076940678785366594…61601005548265799681

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

2.815 × 10¹⁰⁴(105-digit number)

28153881357570733189…23202011096531599359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.815 × 10¹⁰⁴(105-digit number)

28153881357570733189…23202011096531599361

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