Block #855,221

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/16/2014, 4:43:24 AM · Difficulty 10.9685 · 5,971,345 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ce19b386afcf9cf349dbf63f36df3291fd6f65041fd2e3c4d778c32470bffcbc

View on Chainz ↗

Height

#855,221

Difficulty

10.968458

Transactions

Size

2.67 KB

Version

Bits

0af7ece4

Nonce

623,090,326

Timestamp

12/16/2014, 4:43:24 AM

Confirmations

5,971,345

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

48625d7f9691b243f7dcbb4396195b9709e5dab440013bb041f5c308e66ae4a3

Transactions (5)

Coinbase0f0e4284883963…123b5ff48e196f

1 in → 1 out8.3900 XPM116 B

ANSXnLY2…Sd25TjkD

eda840e096af5f…845f58966d2e5e

10 in → 2 out996.0000 XPM1.52 KB

AVkHS2xN…1KELvNC7 AG6g15Lu…okSG4T9k

6e96053c8d2456…af26a7cea8afe8

3 in → 2 out20.1409 XPM523 B

AeveCGBm…8o3QdP1Y ANe3K1D9…6NfZEa1N

17ec4848436199…86870ea4761193

1 in → 2 out0.0632 XPM227 B

AM4QXp6h…8YNhkuBW ARwKubXq…FBtGdkaT

854449c4ea4e3a…f75f6d857ed7bc

1 in → 2 out0.0402 XPM227 B

AeVRprVR…XP4GhJ6a AMXnZejW…eFnwdvA6

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.

2.011 × 10⁹⁷(98-digit number)

20117486076699211298…99043211319554751999

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

2.011 × 10⁹⁷(98-digit number)

20117486076699211298…99043211319554751999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.011 × 10⁹⁷(98-digit number)

20117486076699211298…99043211319554752001

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

4.023 × 10⁹⁷(98-digit number)

40234972153398422596…98086422639109503999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.023 × 10⁹⁷(98-digit number)

40234972153398422596…98086422639109504001

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

8.046 × 10⁹⁷(98-digit number)

80469944306796845192…96172845278219007999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.046 × 10⁹⁷(98-digit number)

80469944306796845192…96172845278219008001

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

1.609 × 10⁹⁸(99-digit number)

16093988861359369038…92345690556438015999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.609 × 10⁹⁸(99-digit number)

16093988861359369038…92345690556438016001

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

3.218 × 10⁹⁸(99-digit number)

32187977722718738076…84691381112876031999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.218 × 10⁹⁸(99-digit number)

32187977722718738076…84691381112876032001

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

6.437 × 10⁹⁸(99-digit number)

64375955445437476153…69382762225752063999

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 #855,221

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