Block #922,284

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 8:45:02 AM · Difficulty 10.9158 · 5,887,293 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

855d622e8e79c04d42dc8a1e1b0b094c08099fec9ae0b1cf109624506a781af6

View on Chainz ↗

Height

#922,284

Difficulty

10.915792

Transactions

Size

115.96 KB

Version

Bits

0aea715c

Nonce

2,782,795,212

Timestamp

2/4/2015, 8:45:02 AM

Confirmations

5,887,293

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

48a10e653e1857286daf7f3414b132ae5251d47cb0512a7ad6a1e0cb43242660

Transactions (5)

Coinbase9f393a6078a48f…65b512cf54b168

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

4f7558b2f56289…f4b90f978ac1e0

200 in → 1 out1074.7933 XPM28.94 KB

AKuP4XsJ…owbodNxQ

ad39c95e3c65f8…1c2c1bcda713e8

200 in → 1 out1021.9533 XPM28.93 KB

AKuP4XsJ…owbodNxQ

8d2c13ade03e80…2c115f7b3a4fd9

200 in → 1 out1041.7679 XPM28.94 KB

AKuP4XsJ…owbodNxQ

8941363b581150…58b7446eaa7a9e

200 in → 1 out897.9714 XPM28.94 KB

AKuP4XsJ…owbodNxQ

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.

3.002 × 10⁹⁶(97-digit number)

30029109725903377653…78879340873209385599

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

3.002 × 10⁹⁶(97-digit number)

30029109725903377653…78879340873209385599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.002 × 10⁹⁶(97-digit number)

30029109725903377653…78879340873209385601

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

6.005 × 10⁹⁶(97-digit number)

60058219451806755306…57758681746418771199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.005 × 10⁹⁶(97-digit number)

60058219451806755306…57758681746418771201

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

1.201 × 10⁹⁷(98-digit number)

12011643890361351061…15517363492837542399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.201 × 10⁹⁷(98-digit number)

12011643890361351061…15517363492837542401

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

2.402 × 10⁹⁷(98-digit number)

24023287780722702122…31034726985675084799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.402 × 10⁹⁷(98-digit number)

24023287780722702122…31034726985675084801

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

4.804 × 10⁹⁷(98-digit number)

48046575561445404245…62069453971350169599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.804 × 10⁹⁷(98-digit number)

48046575561445404245…62069453971350169601

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 #922,284

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