Block #922,266

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 8:15:03 AM · Difficulty 10.9159 · 5,871,875 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

53c81787da8157526417b38811d44b664463201b2d184b4cd90124e0e88aa34b

View on Chainz ↗

Height

#922,266

Difficulty

10.915949

Transactions

Size

116.01 KB

Version

Bits

0aea7b9d

Nonce

1,965,355,950

Timestamp

2/4/2015, 8:15:03 AM

Confirmations

5,871,875

Merkle Root

342ea3cf04925cd1f0f3ea947fec8344270c7ae9432cf20afd15a85392c13d49

Transactions (5)

Coinbase1f871682775226…312142c4eaa42d

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

04d5ec3ee1a8e5…9421abd54eb3ed

200 in → 1 out1002.6109 XPM28.96 KB

AKuP4XsJ…owbodNxQ

f19b2bf8849ff2…99595a4dd268ca

200 in → 1 out970.0756 XPM28.95 KB

AKuP4XsJ…owbodNxQ

b8edf2f47de003…ce798c4044323a

200 in → 1 out964.1841 XPM28.95 KB

AKuP4XsJ…owbodNxQ

d223dc9a2f6e5a…439956647e98c6

200 in → 1 out891.6763 XPM28.95 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.

1.205 × 10⁹⁴(95-digit number)

12050080420356751578…16529717911042674229

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

1.205 × 10⁹⁴(95-digit number)

12050080420356751578…16529717911042674229

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.205 × 10⁹⁴(95-digit number)

12050080420356751578…16529717911042674231

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

2.410 × 10⁹⁴(95-digit number)

24100160840713503157…33059435822085348459

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.410 × 10⁹⁴(95-digit number)

24100160840713503157…33059435822085348461

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

4.820 × 10⁹⁴(95-digit number)

48200321681427006314…66118871644170696919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.820 × 10⁹⁴(95-digit number)

48200321681427006314…66118871644170696921

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

9.640 × 10⁹⁴(95-digit number)

96400643362854012628…32237743288341393839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.640 × 10⁹⁴(95-digit number)

96400643362854012628…32237743288341393841

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

1.928 × 10⁹⁵(96-digit number)

19280128672570802525…64475486576682787679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.928 × 10⁹⁵(96-digit number)

19280128672570802525…64475486576682787681

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