Block #922,367

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/4/2015, 10:21:07 AM · Difficulty 10.9155 · 5,870,211 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b81024f8a8b5d674f6676cfb8527bb9185c46a07c3a86f7874bf5f3c16c2ca0e

View on Chainz ↗

Height

#922,367

Difficulty

10.915546

Transactions

Size

115.97 KB

Version

Bits

0aea613f

Nonce

2,058,049,197

Timestamp

2/4/2015, 10:21:07 AM

Confirmations

5,870,211

Merkle Root

4c9bece4130dcc753df9a40660afacd084b4bb7dc09b655b9f7725e5d048bec5

Transactions (5)

Coinbase5b4463730c724f…bbadbd992e09c0

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

aa5875062f606b…220b9a64967a56

200 in → 1 out1090.9504 XPM28.93 KB

AKuP4XsJ…owbodNxQ

ebfc69c909a94d…50d013c89c9fc0

200 in → 1 out1025.2689 XPM28.94 KB

AKuP4XsJ…owbodNxQ

c7ab3f54da5e7d…23ba62d4353604

200 in → 1 out958.7214 XPM28.95 KB

AKuP4XsJ…owbodNxQ

a0782b7bbb3b4c…b3d1c771977c90

200 in → 1 out904.5083 XPM28.95 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.

4.520 × 10⁹⁶(97-digit number)

45203063178975198308…37912459839558335999

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

4.520 × 10⁹⁶(97-digit number)

45203063178975198308…37912459839558335999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.520 × 10⁹⁶(97-digit number)

45203063178975198308…37912459839558336001

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

9.040 × 10⁹⁶(97-digit number)

90406126357950396616…75824919679116671999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.040 × 10⁹⁶(97-digit number)

90406126357950396616…75824919679116672001

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

1.808 × 10⁹⁷(98-digit number)

18081225271590079323…51649839358233343999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.808 × 10⁹⁷(98-digit number)

18081225271590079323…51649839358233344001

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

3.616 × 10⁹⁷(98-digit number)

36162450543180158646…03299678716466687999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.616 × 10⁹⁷(98-digit number)

36162450543180158646…03299678716466688001

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

7.232 × 10⁹⁷(98-digit number)

72324901086360317292…06599357432933375999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.232 × 10⁹⁷(98-digit number)

72324901086360317292…06599357432933376001

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

1.446 × 10⁹⁸(99-digit number)

14464980217272063458…13198714865866751999

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