Block #922,368

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 10:23:11 AM · Difficulty 10.9155 · 5,872,663 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

08a1d09faf9e2f720022a981e2d2c9fdd93e6d4b2c3b31d5d726207a0b4429e8

View on Chainz ↗

Height

#922,368

Difficulty

10.915536

Transactions

Size

116.00 KB

Version

Bits

0aea6089

Nonce

1,738,212,092

Timestamp

2/4/2015, 10:23:11 AM

Confirmations

5,872,663

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

a80e3cff82b34939b674accd5e9a2ca70b3b3eb61af881fb6f07d8fd048ee98d

Transactions (5)

Coinbased8e136da9e9617…0452416314a35c

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

beae723cb43fac…62c4fd3ff24747

200 in → 1 out1161.4076 XPM28.98 KB

AKuP4XsJ…owbodNxQ

6a90e673d0ac7b…f46b34505c02be

200 in → 1 out1028.0770 XPM28.94 KB

AKuP4XsJ…owbodNxQ

1a215184a6e775…cdc9ca780cd5c9

200 in → 1 out1107.1285 XPM28.94 KB

AKuP4XsJ…owbodNxQ

a701b422068318…fd17980a92a435

200 in → 1 out854.9454 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.

1.247 × 10⁹⁷(98-digit number)

12471998522949645271…64037116928001364479

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

1.247 × 10⁹⁷(98-digit number)

12471998522949645271…64037116928001364479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.247 × 10⁹⁷(98-digit number)

12471998522949645271…64037116928001364481

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

2.494 × 10⁹⁷(98-digit number)

24943997045899290542…28074233856002728959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.494 × 10⁹⁷(98-digit number)

24943997045899290542…28074233856002728961

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

4.988 × 10⁹⁷(98-digit number)

49887994091798581084…56148467712005457919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.988 × 10⁹⁷(98-digit number)

49887994091798581084…56148467712005457921

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

9.977 × 10⁹⁷(98-digit number)

99775988183597162168…12296935424010915839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.977 × 10⁹⁷(98-digit number)

99775988183597162168…12296935424010915841

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

1.995 × 10⁹⁸(99-digit number)

19955197636719432433…24593870848021831679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.995 × 10⁹⁸(99-digit number)

19955197636719432433…24593870848021831681

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