Block #360,477

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/15/2014, 11:34:53 AM · Difficulty 10.3937 · 6,449,980 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d3f5843a948c85c7e183384af1d3e7017ae67e5fe2ab5b71f3c012975ea63487

View on Chainz ↗

Height

#360,477

Difficulty

10.393658

Transactions

Size

885 B

Version

Bits

0a64c6cd

Nonce

16,778,601

Timestamp

1/15/2014, 11:34:53 AM

Confirmations

6,449,980

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

947252d804e5f0d3f272739eec84a9c635f7c6f44935216661f560f242e7f46f

Transactions (4)

Coinbasebf32204f95a11c…d685717a0b8ccc

1 in → 1 out9.2700 XPM116 B

AbwWkWZt…kawDhufa

4ef59d4827668a…30d47c97d865ae

1 in → 2 out9.2500 XPM227 B

AVLAduET…3uVBURM2 ARoXNQ3w…jzfzkW9U

68cb6c6b29c328…03cd966093d906

1 in → 2 out9.2500 XPM226 B

AS6ixCbY…Pmo14Y1U AeBofmLx…jGyTMm8P

62bee5fc85d84d…d7e5421a4897d6

1 in → 2 out3.0127 XPM226 B

ANECCeuu…mJ6mJJWN ATmuR96V…9kaCrCEc

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.

8.448 × 10⁹⁴(95-digit number)

84481996707124097441…07211911829227449299

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

8.448 × 10⁹⁴(95-digit number)

84481996707124097441…07211911829227449299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.448 × 10⁹⁴(95-digit number)

84481996707124097441…07211911829227449301

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

1.689 × 10⁹⁵(96-digit number)

16896399341424819488…14423823658454898599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.689 × 10⁹⁵(96-digit number)

16896399341424819488…14423823658454898601

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

3.379 × 10⁹⁵(96-digit number)

33792798682849638976…28847647316909797199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.379 × 10⁹⁵(96-digit number)

33792798682849638976…28847647316909797201

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

6.758 × 10⁹⁵(96-digit number)

67585597365699277953…57695294633819594399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.758 × 10⁹⁵(96-digit number)

67585597365699277953…57695294633819594401

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

1.351 × 10⁹⁶(97-digit number)

13517119473139855590…15390589267639188799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.351 × 10⁹⁶(97-digit number)

13517119473139855590…15390589267639188801

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 #360,477

Cookie Preferences