Block #866,884

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/24/2014, 9:49:26 PM · Difficulty 10.9628 · 5,941,054 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

80b51442b3197048725701c39237ae6fee3d71f1b09e1c3d82aea12bccd7e783

View on Chainz ↗

Height

#866,884

Difficulty

10.962807

Transactions

Size

1.73 KB

Version

Bits

0af67a82

Nonce

50,455,403

Timestamp

12/24/2014, 9:49:26 PM

Confirmations

5,941,054

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

83dffcb7461d9a82aad29c3f637ce83a85d39b949aebf9cdc9c69050917d9d32

Transactions (4)

Coinbased4cf4b41af613d…949a290532bb16

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

32402e30f57407…4214ffee9d11a1

2 in → 2 out46.9100 XPM375 B

AbfEn7Nt…55CdqUCR AMTLGRW9…FB1ruKUp

78499b8c0356f1…5600fdd33cfae2

6 in → 2 out5.0144 XPM967 B

APJQunho…CWiUv3PV ARepD4Pg…FnabeUUu

2ed0b625d1e5c7…f8f1a1fa64ddeb

1 in → 2 out1.6870 XPM225 B

ALP6szJY…eEPSo5sX AWPSAZaD…isueRV8y

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.

6.921 × 10⁹³(94-digit number)

69213741652227304296…91352239193446128799

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

6.921 × 10⁹³(94-digit number)

69213741652227304296…91352239193446128799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.921 × 10⁹³(94-digit number)

69213741652227304296…91352239193446128801

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

1.384 × 10⁹⁴(95-digit number)

13842748330445460859…82704478386892257599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.384 × 10⁹⁴(95-digit number)

13842748330445460859…82704478386892257601

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

2.768 × 10⁹⁴(95-digit number)

27685496660890921718…65408956773784515199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.768 × 10⁹⁴(95-digit number)

27685496660890921718…65408956773784515201

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

5.537 × 10⁹⁴(95-digit number)

55370993321781843436…30817913547569030399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.537 × 10⁹⁴(95-digit number)

55370993321781843436…30817913547569030401

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

1.107 × 10⁹⁵(96-digit number)

11074198664356368687…61635827095138060799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.107 × 10⁹⁵(96-digit number)

11074198664356368687…61635827095138060801

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

2.214 × 10⁹⁵(96-digit number)

22148397328712737374…23271654190276121599

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 #866,884

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