Block #922,360

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 10:15:26 AM · Difficulty 10.9155 · 5,870,662 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2c07525ac89f324f279d844695b999576b3769970d81d005d374938b2779bc44

View on Chainz ↗

Height

#922,360

Difficulty

10.915505

Transactions

Size

116.00 KB

Version

Bits

0aea5e82

Nonce

902,308,887

Timestamp

2/4/2015, 10:15:26 AM

Confirmations

5,870,662

Merkle Root

12562d1d5c82cf5a02b409bd3d39a1e187281cd9c2a41342aa4f163529209eeb

Transactions (5)

Coinbase304b2f5ed37746…80a7a13c211af0

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

fe7e03a5e02f02…8f73d9081fc4ce

200 in → 1 out1055.9370 XPM28.96 KB

AKuP4XsJ…owbodNxQ

e4edfb7b207f64…c1205e2e10d4c5

200 in → 1 out1035.6892 XPM28.94 KB

AKuP4XsJ…owbodNxQ

7f6883f24b79cf…f44e1ab766d330

200 in → 1 out970.4088 XPM28.94 KB

AKuP4XsJ…owbodNxQ

9d6650347961e7…881551542780a0

200 in → 1 out1009.4736 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.

2.932 × 10⁹⁵(96-digit number)

29327442619283785666…59197979614735948649

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

2.932 × 10⁹⁵(96-digit number)

29327442619283785666…59197979614735948649

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.932 × 10⁹⁵(96-digit number)

29327442619283785666…59197979614735948651

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

5.865 × 10⁹⁵(96-digit number)

58654885238567571332…18395959229471897299

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.865 × 10⁹⁵(96-digit number)

58654885238567571332…18395959229471897301

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

1.173 × 10⁹⁶(97-digit number)

11730977047713514266…36791918458943794599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.173 × 10⁹⁶(97-digit number)

11730977047713514266…36791918458943794601

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

2.346 × 10⁹⁶(97-digit number)

23461954095427028533…73583836917887589199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.346 × 10⁹⁶(97-digit number)

23461954095427028533…73583836917887589201

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

4.692 × 10⁹⁶(97-digit number)

46923908190854057066…47167673835775178399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.692 × 10⁹⁶(97-digit number)

46923908190854057066…47167673835775178401

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