Block #922,386

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 10:43:27 AM · Difficulty 10.9155 · 5,873,078 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

df4d8de4afe8d5a5f1adcdac7e1d5a8e4e1a9b6af24c8e0b300a648c11e46c54

View on Chainz ↗

Height

#922,386

Difficulty

10.915466

Transactions

Size

115.98 KB

Version

Bits

0aea5bf7

Nonce

229,558,850

Timestamp

2/4/2015, 10:43:27 AM

Confirmations

5,873,078

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

5b570d641e1018a49cd89897fbd7ed4a6c1114da17eafc4889196529bf11ad34

Transactions (5)

Coinbasea216b45a68c5b8…ca025997a68c90

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

150fdd4cd39fcf…02c3dfaf5c0e0d

200 in → 1 out1199.2919 XPM28.95 KB

AKuP4XsJ…owbodNxQ

270dc1c0ab017b…8cb512b997808c

200 in → 1 out924.1415 XPM28.94 KB

AKuP4XsJ…owbodNxQ

45bcda32d4d87d…6ec67b16c24722

200 in → 1 out1083.6184 XPM28.94 KB

AKuP4XsJ…owbodNxQ

d03555aa5f43a2…d9c7e42e8171e6

200 in → 1 out998.3990 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.

6.124 × 10⁹⁶(97-digit number)

61248136471450875771…43655455283565583359

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

6.124 × 10⁹⁶(97-digit number)

61248136471450875771…43655455283565583359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.124 × 10⁹⁶(97-digit number)

61248136471450875771…43655455283565583361

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

1.224 × 10⁹⁷(98-digit number)

12249627294290175154…87310910567131166719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.224 × 10⁹⁷(98-digit number)

12249627294290175154…87310910567131166721

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

2.449 × 10⁹⁷(98-digit number)

24499254588580350308…74621821134262333439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.449 × 10⁹⁷(98-digit number)

24499254588580350308…74621821134262333441

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

4.899 × 10⁹⁷(98-digit number)

48998509177160700617…49243642268524666879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.899 × 10⁹⁷(98-digit number)

48998509177160700617…49243642268524666881

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

9.799 × 10⁹⁷(98-digit number)

97997018354321401234…98487284537049333759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.799 × 10⁹⁷(98-digit number)

97997018354321401234…98487284537049333761

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