Block #848,591

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/11/2014, 4:56:53 AM · Difficulty 10.9716 · 5,994,136 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b3323c02218230995e96f8540f75bff629aa390e58195581a2866f0d24b31f64

View on Chainz ↗

Height

#848,591

Difficulty

10.971559

Transactions

Size

884 B

Version

Bits

0af8b819

Nonce

732,964,631

Timestamp

12/11/2014, 4:56:53 AM

Confirmations

5,994,136

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

7ca4ea4b6498f74343ee98f87eb580de21f0c8aac6473d35690b8531425be60b

Transactions (4)

Coinbase4d9204dfc48220…27da659b8ebaac

1 in → 1 out8.3350 XPM116 B

ANSXnLY2…Sd25TjkD

37073a9de186a4…d3a1b27a9c00af

1 in → 2 out0.1234 XPM225 B

AXiFZuCn…txfWDHBB AVC9Q5uu…Kc4kR9cc

4e217fe531b411…a6d829a8b1b2ee

1 in → 2 out0.1232 XPM226 B

AcZUn9fa…T7JjNbKo AMqEiFSN…CSNTyhWm

0eddab3b904ad1…28e9d5f82f799d

1 in → 2 out0.1240 XPM226 B

AbBnqFAP…1iBiDCRy AccRgcaG…CD2CAAT5

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.

9.931 × 10⁹⁵(96-digit number)

99318379864895485030…74145872740082038959

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

9.931 × 10⁹⁵(96-digit number)

99318379864895485030…74145872740082038959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.931 × 10⁹⁵(96-digit number)

99318379864895485030…74145872740082038961

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

1.986 × 10⁹⁶(97-digit number)

19863675972979097006…48291745480164077919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.986 × 10⁹⁶(97-digit number)

19863675972979097006…48291745480164077921

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

3.972 × 10⁹⁶(97-digit number)

39727351945958194012…96583490960328155839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.972 × 10⁹⁶(97-digit number)

39727351945958194012…96583490960328155841

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

7.945 × 10⁹⁶(97-digit number)

79454703891916388024…93166981920656311679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.945 × 10⁹⁶(97-digit number)

79454703891916388024…93166981920656311681

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

1.589 × 10⁹⁷(98-digit number)

15890940778383277604…86333963841312623359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.589 × 10⁹⁷(98-digit number)

15890940778383277604…86333963841312623361

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 #848,591

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