Block #841,274

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/5/2014, 6:25:45 PM · Difficulty 10.9741 · 5,999,011 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5f2e7739fda4568f8973a385a7dc1e4fc323d67f8eb3025814a3f1e0d3bd9a43

View on Chainz ↗

Height

#841,274

Difficulty

10.974109

Transactions

Size

432 B

Version

Bits

0af95f32

Nonce

2,189,768,194

Timestamp

12/5/2014, 6:25:45 PM

Confirmations

5,999,011

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

73bb3a2881f3e16381066ed0d705a4eb7d1192f23cfc8d76bad9ff61db765888

Transactions (2)

Coinbase0b84596f682325…3b0efcf8a4ab48

1 in → 1 out8.3050 XPM116 B

ANSXnLY2…Sd25TjkD

37ff3525449e90…4306193d140078

1 in → 2 out0.9369 XPM225 B

AXTrYMNF…FaxHuur7 APANSr4b…XeVG1upq

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.

1.210 × 10⁹⁸(99-digit number)

12107619003948939773…23652134451698585599

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

1.210 × 10⁹⁸(99-digit number)

12107619003948939773…23652134451698585599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.210 × 10⁹⁸(99-digit number)

12107619003948939773…23652134451698585601

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

2.421 × 10⁹⁸(99-digit number)

24215238007897879547…47304268903397171199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.421 × 10⁹⁸(99-digit number)

24215238007897879547…47304268903397171201

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

4.843 × 10⁹⁸(99-digit number)

48430476015795759095…94608537806794342399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.843 × 10⁹⁸(99-digit number)

48430476015795759095…94608537806794342401

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

9.686 × 10⁹⁸(99-digit number)

96860952031591518190…89217075613588684799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.686 × 10⁹⁸(99-digit number)

96860952031591518190…89217075613588684801

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

1.937 × 10⁹⁹(100-digit number)

19372190406318303638…78434151227177369599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.937 × 10⁹⁹(100-digit number)

19372190406318303638…78434151227177369601

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

3.874 × 10⁹⁹(100-digit number)

38744380812636607276…56868302454354739199

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 #841,274

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