Block #922,443

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/4/2015, 11:50:14 AM · Difficulty 10.9153 · 5,871,847 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a4521a05b2cbc50caf88e9a6a51884d8901669b4e0663b815d47f61a1be14b29

View on Chainz ↗

Height

#922,443

Difficulty

10.915313

Transactions

Size

116.03 KB

Version

Bits

0aea51f2

Nonce

118,728,188

Timestamp

2/4/2015, 11:50:14 AM

Confirmations

5,871,847

Merkle Root

888c1847ed2cda98c80a26a3cc011c26b02685e119b0cbd61f1f6094d5fcc1e9

Transactions (5)

Coinbase5e5befe4b1c4e2…0c26228f82603e

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

fb0c71f8031ac9…705ba389c90ac3

200 in → 1 out1041.5698 XPM28.96 KB

AKuP4XsJ…owbodNxQ

a88ab99bad4aaf…4995314a83a272

200 in → 1 out1012.6131 XPM28.96 KB

AKuP4XsJ…owbodNxQ

8155b9a62c083c…97545f50860c0b

200 in → 1 out1011.2260 XPM28.96 KB

AKuP4XsJ…owbodNxQ

9172a735443869…0a16b9682aecd1

200 in → 1 out934.8040 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.

1.966 × 10⁹⁹(100-digit number)

19665055376114209652…52189241761503805439

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

1.966 × 10⁹⁹(100-digit number)

19665055376114209652…52189241761503805439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.966 × 10⁹⁹(100-digit number)

19665055376114209652…52189241761503805441

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

3.933 × 10⁹⁹(100-digit number)

39330110752228419305…04378483523007610879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.933 × 10⁹⁹(100-digit number)

39330110752228419305…04378483523007610881

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

7.866 × 10⁹⁹(100-digit number)

78660221504456838611…08756967046015221759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.866 × 10⁹⁹(100-digit number)

78660221504456838611…08756967046015221761

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

1.573 × 10¹⁰⁰(101-digit number)

15732044300891367722…17513934092030443519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.573 × 10¹⁰⁰(101-digit number)

15732044300891367722…17513934092030443521

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

3.146 × 10¹⁰⁰(101-digit number)

31464088601782735444…35027868184060887039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.146 × 10¹⁰⁰(101-digit number)

31464088601782735444…35027868184060887041

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

6.292 × 10¹⁰⁰(101-digit number)

62928177203565470888…70055736368121774079

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