Block #854,417

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/15/2014, 2:48:42 PM · Difficulty 10.9686 · 5,989,583 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

832f359ec74739f3536234c3b097ae67a0c14b50821bab0250779360149589e5

View on Chainz ↗

Height

#854,417

Difficulty

10.968627

Transactions

Size

433 B

Version

Bits

0af7f7f5

Nonce

42,540,077

Timestamp

12/15/2014, 2:48:42 PM

Confirmations

5,989,583

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e4a6c3317981c4541192e49c46a9894cca3c01eec54fe6ceff783acee348a706

Transactions (2)

Coinbase2ff9e0e6e5e975…6794a9ed9cb057

1 in → 1 out8.3150 XPM116 B

ANSXnLY2…Sd25TjkD

59d05d1e597d18…ecfa85224d048a

1 in → 2 out0.0901 XPM227 B

ASrBhwfp…kbdpULGR AHnvxEMm…fAuqMECg

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.

9.625 × 10⁹⁵(96-digit number)

96257532947128728504…23824387190183733759

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

9.625 × 10⁹⁵(96-digit number)

96257532947128728504…23824387190183733759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.625 × 10⁹⁵(96-digit number)

96257532947128728504…23824387190183733761

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

1.925 × 10⁹⁶(97-digit number)

19251506589425745700…47648774380367467519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.925 × 10⁹⁶(97-digit number)

19251506589425745700…47648774380367467521

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

3.850 × 10⁹⁶(97-digit number)

38503013178851491401…95297548760734935039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.850 × 10⁹⁶(97-digit number)

38503013178851491401…95297548760734935041

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

7.700 × 10⁹⁶(97-digit number)

77006026357702982803…90595097521469870079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.700 × 10⁹⁶(97-digit number)

77006026357702982803…90595097521469870081

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

1.540 × 10⁹⁷(98-digit number)

15401205271540596560…81190195042939740159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.540 × 10⁹⁷(98-digit number)

15401205271540596560…81190195042939740161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.080 × 10⁹⁷(98-digit number)

30802410543081193121…62380390085879480319

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #854,417

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