Block #922,320

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/4/2015, 9:31:50 AM · Difficulty 10.9156 · 5,869,576 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1f2dcbfcbb9532493ba98b7bdadab78673a52eaec73b10ef768caaab463960c4

View on Chainz ↗

Height

#922,320

Difficulty

10.915571

Transactions

Size

115.96 KB

Version

Bits

0aea62e4

Nonce

302,649,506

Timestamp

2/4/2015, 9:31:50 AM

Confirmations

5,869,576

Merkle Root

45a73bbfddb264e99042f514135a49521df1662fa09b8223c20024c2822b1e10

Transactions (5)

Coinbase57d1e6afd3db14…814304f44a296c

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

b0476fd4c83e3f…273c759c02b1c2

200 in → 1 out1089.0970 XPM28.94 KB

AKuP4XsJ…owbodNxQ

8833bf1afa0fa4…cc402cab0c4216

200 in → 1 out980.1283 XPM28.94 KB

AKuP4XsJ…owbodNxQ

86207480ee4039…fd6a96a6cf1e8d

200 in → 1 out957.8146 XPM28.94 KB

AKuP4XsJ…owbodNxQ

73be227deb4426…b1afeb92260fa0

200 in → 1 out1056.7765 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.

2.023 × 10⁹⁵(96-digit number)

20236945889051805958…41998587145328434739

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

2.023 × 10⁹⁵(96-digit number)

20236945889051805958…41998587145328434739

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.023 × 10⁹⁵(96-digit number)

20236945889051805958…41998587145328434741

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

4.047 × 10⁹⁵(96-digit number)

40473891778103611916…83997174290656869479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.047 × 10⁹⁵(96-digit number)

40473891778103611916…83997174290656869481

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

8.094 × 10⁹⁵(96-digit number)

80947783556207223833…67994348581313738959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.094 × 10⁹⁵(96-digit number)

80947783556207223833…67994348581313738961

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

1.618 × 10⁹⁶(97-digit number)

16189556711241444766…35988697162627477919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.618 × 10⁹⁶(97-digit number)

16189556711241444766…35988697162627477921

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

3.237 × 10⁹⁶(97-digit number)

32379113422482889533…71977394325254955839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.237 × 10⁹⁶(97-digit number)

32379113422482889533…71977394325254955841

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

6.475 × 10⁹⁶(97-digit number)

64758226844965779066…43954788650509911679

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