Block #448,409

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/17/2014, 9:48:56 PM · Difficulty 10.3680 · 6,361,070 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

08862844783b84788757c4d32abaa95988dbcf2d7dae377d06da6255da797ac3

View on Chainz ↗

Height

#448,409

Difficulty

10.368022

Transactions

Size

1.00 KB

Version

Bits

0a5e36aa

Nonce

187,465

Timestamp

3/17/2014, 9:48:56 PM

Confirmations

6,361,070

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

69bddc23540ea4494abd93ad8bd6fdda16589e1e5b3c6dad2d4bc972aaf117e9

Transactions (4)

Coinbaseaf32ab114bf5a6…92752c496990ab

1 in → 1 out9.3200 XPM110 B

AeKNrjNj…1NEq95Ta

11580afebd076f…1a079916802af6

2 in → 2 out11.0108 XPM375 B

AU1fG3ZU…VavhwYTd AdAuA2Pe…HSbaBW8J

fa4d15101afeed…cfaba7fe8a4a0d

1 in → 2 out7.2664 XPM226 B

AViJiBwS…fUTcEFfq AcXRTCxQ…wsNNMAoH

b35bd32df3827c…5332456cbaf6eb

1 in → 2 out5.2391 XPM225 B

ALWg8jYK…f2SA1ZM9 AYBs9UTC…odqRGSpW

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.

4.254 × 10⁹⁶(97-digit number)

42547893463013761198…71533848451841390079

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

4.254 × 10⁹⁶(97-digit number)

42547893463013761198…71533848451841390079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.254 × 10⁹⁶(97-digit number)

42547893463013761198…71533848451841390081

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

8.509 × 10⁹⁶(97-digit number)

85095786926027522397…43067696903682780159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.509 × 10⁹⁶(97-digit number)

85095786926027522397…43067696903682780161

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

1.701 × 10⁹⁷(98-digit number)

17019157385205504479…86135393807365560319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.701 × 10⁹⁷(98-digit number)

17019157385205504479…86135393807365560321

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

3.403 × 10⁹⁷(98-digit number)

34038314770411008959…72270787614731120639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.403 × 10⁹⁷(98-digit number)

34038314770411008959…72270787614731120641

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

6.807 × 10⁹⁷(98-digit number)

68076629540822017918…44541575229462241279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.807 × 10⁹⁷(98-digit number)

68076629540822017918…44541575229462241281

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 #448,409

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