Block #325,946

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/23/2013, 10:35:53 AM · Difficulty 10.1955 · 6,489,164 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f451c485ca21edd9e75685acaf825b8a642a7852df5c13b4caf0a79c39683386

View on Chainz ↗

Height

#325,946

Difficulty

10.195529

Transactions

Size

1.72 KB

Version

Bits

0a320e2d

Nonce

10,817

Timestamp

12/23/2013, 10:35:53 AM

Confirmations

6,489,164

Mined by

⛏️ P2SHAdptcEaAPKNsvPpoeFA7eUkt46FbaHW1gj

Merkle Root

012251f813e676f47de8353b67ee1bbcd2aec76e6f15048fbd14b697c157110f

Transactions (3)

Coinbase0bd3bba6fccd62…82ede03ad97ac2

1 in → 1 out9.6400 XPM110 B

AdptcEaA…FbaHW1gj

5591047e835b6a…9e8bdf2b6d03cd

8 in → 5 out12.1353 XPM1.30 KB

AGVxdvqN…9hywpG61 APQKXjUv…hEDARNUA AeKNrjNj…1NEq95Ta AJNWihF1…ZbvMRVEB AazfaUAJ…WaQjuUwm

3a7bc974f2a6f9…c812885e3c99c2

1 in → 2 out7.5737 XPM227 B

AacCxhLG…uAbVU19P AMBaesuK…6AGZoQG4

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.

3.592 × 10⁹⁹(100-digit number)

35926733696067644029…10635519154984581159

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

3.592 × 10⁹⁹(100-digit number)

35926733696067644029…10635519154984581159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.592 × 10⁹⁹(100-digit number)

35926733696067644029…10635519154984581161

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

7.185 × 10⁹⁹(100-digit number)

71853467392135288059…21271038309969162319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.185 × 10⁹⁹(100-digit number)

71853467392135288059…21271038309969162321

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

1.437 × 10¹⁰⁰(101-digit number)

14370693478427057611…42542076619938324639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.437 × 10¹⁰⁰(101-digit number)

14370693478427057611…42542076619938324641

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

2.874 × 10¹⁰⁰(101-digit number)

28741386956854115223…85084153239876649279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.874 × 10¹⁰⁰(101-digit number)

28741386956854115223…85084153239876649281

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

5.748 × 10¹⁰⁰(101-digit number)

57482773913708230447…70168306479753298559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.748 × 10¹⁰⁰(101-digit number)

57482773913708230447…70168306479753298561

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 #325,946

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