Block #922,474

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 12:25:53 PM · Difficulty 10.9153 · 5,869,879 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7d76211c1ed0218270df0e06470445b8cf3afda43d3a23b622d32dc7b6e5871a

View on Chainz ↗

Height

#922,474

Difficulty

10.915252

Transactions

Size

116.04 KB

Version

Bits

0aea4def

Nonce

1,404,021,616

Timestamp

2/4/2015, 12:25:53 PM

Confirmations

5,869,879

Merkle Root

328c8126030d38cb479886bc15aee6cf3c2303350835925b68f6d112df52624f

Transactions (5)

Coinbase7658f35e99835e…0530ec7a7093cc

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

6d5d00b90943e0…fa288923a40d52

200 in → 1 out943.0561 XPM28.96 KB

AKuP4XsJ…owbodNxQ

84429d8d9dc22b…5da33b274f5878

200 in → 1 out1007.4541 XPM28.96 KB

AKuP4XsJ…owbodNxQ

be37a77668b025…b655c902abe933

200 in → 1 out1038.7559 XPM28.96 KB

AKuP4XsJ…owbodNxQ

66b4689a0ac72d…f4d3a7e6342646

200 in → 1 out997.0974 XPM28.96 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.

7.637 × 10⁹⁵(96-digit number)

76371192662027452038…98564182886460152639

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

7.637 × 10⁹⁵(96-digit number)

76371192662027452038…98564182886460152639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.637 × 10⁹⁵(96-digit number)

76371192662027452038…98564182886460152641

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

1.527 × 10⁹⁶(97-digit number)

15274238532405490407…97128365772920305279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.527 × 10⁹⁶(97-digit number)

15274238532405490407…97128365772920305281

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

3.054 × 10⁹⁶(97-digit number)

30548477064810980815…94256731545840610559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.054 × 10⁹⁶(97-digit number)

30548477064810980815…94256731545840610561

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

6.109 × 10⁹⁶(97-digit number)

61096954129621961630…88513463091681221119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.109 × 10⁹⁶(97-digit number)

61096954129621961630…88513463091681221121

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

1.221 × 10⁹⁷(98-digit number)

12219390825924392326…77026926183362442239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.221 × 10⁹⁷(98-digit number)

12219390825924392326…77026926183362442241

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