Block #922,349

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 10:03:05 AM · Difficulty 10.9155 · 5,869,563 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1da769bf36e6741d64873ed52e276ab166e331d49c2884dec169170a1f9f3f56

View on Chainz ↗

Height

#922,349

Difficulty

10.915536

Transactions

Size

115.97 KB

Version

Bits

0aea6093

Nonce

612,645,534

Timestamp

2/4/2015, 10:03:05 AM

Confirmations

5,869,563

Merkle Root

1417aebc4f9eb372e5cfcdc3c7743c8df5c5260ada8e1507191ab4bd1c37266b

Transactions (5)

Coinbasee26715e749f45c…1ce393a5c1afd0

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

d14ccaa721efa0…3a2bea8dc8ec0e

200 in → 1 out1105.7990 XPM28.95 KB

AKuP4XsJ…owbodNxQ

8046be779ce960…1b33ee7dabf2a9

200 in → 1 out1008.7066 XPM28.94 KB

AKuP4XsJ…owbodNxQ

13e82d71175acb…2120da3c2e402b

200 in → 1 out938.6063 XPM28.94 KB

AKuP4XsJ…owbodNxQ

e8f0aeb30c27be…887e63af3e8572

200 in → 1 out1071.8523 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.

4.149 × 10⁹⁴(95-digit number)

41498500832147489992…64309755324580452959

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

4.149 × 10⁹⁴(95-digit number)

41498500832147489992…64309755324580452959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.149 × 10⁹⁴(95-digit number)

41498500832147489992…64309755324580452961

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

8.299 × 10⁹⁴(95-digit number)

82997001664294979985…28619510649160905919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.299 × 10⁹⁴(95-digit number)

82997001664294979985…28619510649160905921

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

1.659 × 10⁹⁵(96-digit number)

16599400332858995997…57239021298321811839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.659 × 10⁹⁵(96-digit number)

16599400332858995997…57239021298321811841

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

3.319 × 10⁹⁵(96-digit number)

33198800665717991994…14478042596643623679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.319 × 10⁹⁵(96-digit number)

33198800665717991994…14478042596643623681

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

6.639 × 10⁹⁵(96-digit number)

66397601331435983988…28956085193287247359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.639 × 10⁹⁵(96-digit number)

66397601331435983988…28956085193287247361

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