Block #854,250

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/15/2014, 11:59:05 AM · Difficulty 10.9686 · 5,971,310 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b41f3f703b5580a74118dbf7d216138e671720c75b63646e4d8a0318f01903b4

View on Chainz ↗

Height

#854,250

Difficulty

10.968641

Transactions

Size

997 B

Version

Bits

0af7f8d3

Nonce

1,574,655,069

Timestamp

12/15/2014, 11:59:05 AM

Confirmations

5,971,310

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

3099cb8d1a72367dd09943c2b8e4eac35badabf87f3c5db250ef7a84ad647812

Transactions (4)

Coinbasef1d544926c2b23…ba1646a0aa43f3

1 in → 1 out8.3381 XPM116 B

ANSXnLY2…Sd25TjkD

ffc2ea677d8eea…312207408162df

2 in → 2 out10.8090 XPM374 B

AS5kbTkt…sQP56TZ6 AWAbb2pL…4Wmht5QK

914c2cb4fdc121…18d818cd732ac6

1 in → 2 out5.1451 XPM225 B

AUHRvbhb…EsmHh1Nc AYrwBKyU…1S6w2wRP

dd09340be47135…86888bc6cef9fd

1 in → 1 out0.0105 XPM192 B

AVYTMEEW…EMqCTNFR

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.

1.037 × 10⁹⁵(96-digit number)

10373729705849408174…40873877233954185799

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

1.037 × 10⁹⁵(96-digit number)

10373729705849408174…40873877233954185799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.037 × 10⁹⁵(96-digit number)

10373729705849408174…40873877233954185801

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

2.074 × 10⁹⁵(96-digit number)

20747459411698816348…81747754467908371599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.074 × 10⁹⁵(96-digit number)

20747459411698816348…81747754467908371601

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

4.149 × 10⁹⁵(96-digit number)

41494918823397632697…63495508935816743199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.149 × 10⁹⁵(96-digit number)

41494918823397632697…63495508935816743201

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

8.298 × 10⁹⁵(96-digit number)

82989837646795265394…26991017871633486399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.298 × 10⁹⁵(96-digit number)

82989837646795265394…26991017871633486401

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

1.659 × 10⁹⁶(97-digit number)

16597967529359053078…53982035743266972799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.659 × 10⁹⁶(97-digit number)

16597967529359053078…53982035743266972801

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 #854,250

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