Block #922,492

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 12:47:22 PM · Difficulty 10.9152 · 5,870,493 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b5b28b69b63870ceae8f817e53f939e9a6d00f32a2ca972a10d17aa9b00239e8

View on Chainz ↗

Height

#922,492

Difficulty

10.915182

Transactions

Size

116.07 KB

Version

Bits

0aea4961

Nonce

94,343,935

Timestamp

2/4/2015, 12:47:22 PM

Confirmations

5,870,493

Merkle Root

5ba1b4533e75d30dfdb9a9d5cba8e30492ee6e993276e2b4e1f6e10814f54c9c

Transactions (5)

Coinbase47aa081e19b441…09602c4480f20f

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

155b361379c928…f5e701c8237555

200 in → 1 out1123.3489 XPM28.97 KB

AKuP4XsJ…owbodNxQ

5550b90048c81a…c53c7521e75896

200 in → 1 out1013.1350 XPM28.96 KB

AKuP4XsJ…owbodNxQ

18146ebd502a2f…541b45797dd83a

200 in → 1 out996.9319 XPM28.96 KB

AKuP4XsJ…owbodNxQ

33a6fda37f295a…1c6d727ba3e08b

200 in → 1 out983.2926 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.

1.864 × 10⁹⁹(100-digit number)

18640544474924835279…14618651875596287999

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

1.864 × 10⁹⁹(100-digit number)

18640544474924835279…14618651875596287999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.864 × 10⁹⁹(100-digit number)

18640544474924835279…14618651875596288001

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

3.728 × 10⁹⁹(100-digit number)

37281088949849670558…29237303751192575999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.728 × 10⁹⁹(100-digit number)

37281088949849670558…29237303751192576001

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

7.456 × 10⁹⁹(100-digit number)

74562177899699341117…58474607502385151999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.456 × 10⁹⁹(100-digit number)

74562177899699341117…58474607502385152001

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

1.491 × 10¹⁰⁰(101-digit number)

14912435579939868223…16949215004770303999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.491 × 10¹⁰⁰(101-digit number)

14912435579939868223…16949215004770304001

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

2.982 × 10¹⁰⁰(101-digit number)

29824871159879736447…33898430009540607999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.982 × 10¹⁰⁰(101-digit number)

29824871159879736447…33898430009540608001

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