Block #922,270

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/4/2015, 8:23:07 AM · Difficulty 10.9159 · 5,881,129 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7b153a5ceb647c06821c72eb69fe23c3920f9b7c7f07d773b86b5a19916a3e43

View on Chainz ↗

Height

#922,270

Difficulty

10.915862

Transactions

Size

116.03 KB

Version

Bits

0aea75eb

Nonce

455,931,402

Timestamp

2/4/2015, 8:23:07 AM

Confirmations

5,881,129

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

cf884d83e9ad6c122ce7c1c7a3b54f53f25fbc1560f41873e38f9cc4f6bd827e

Transactions (5)

Coinbase9f296e9801ddc1…2eeaf3fe7dc5f4

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

f825448b0cdca8…ffe443a61778a5

200 in → 1 out1148.5763 XPM28.98 KB

AKuP4XsJ…owbodNxQ

9ec01edf8c0712…de1408d47d86a0

200 in → 1 out883.7422 XPM28.95 KB

AKuP4XsJ…owbodNxQ

f318f74d8b70bf…d2c310cba18810

200 in → 1 out1078.4372 XPM28.95 KB

AKuP4XsJ…owbodNxQ

11be5cdba2dda4…667779757b4f99

200 in → 1 out939.5622 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.

1.847 × 10⁹⁷(98-digit number)

18473782480608228357…83195327752427731839

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

1.847 × 10⁹⁷(98-digit number)

18473782480608228357…83195327752427731839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.847 × 10⁹⁷(98-digit number)

18473782480608228357…83195327752427731841

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

3.694 × 10⁹⁷(98-digit number)

36947564961216456714…66390655504855463679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.694 × 10⁹⁷(98-digit number)

36947564961216456714…66390655504855463681

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

7.389 × 10⁹⁷(98-digit number)

73895129922432913429…32781311009710927359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.389 × 10⁹⁷(98-digit number)

73895129922432913429…32781311009710927361

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

1.477 × 10⁹⁸(99-digit number)

14779025984486582685…65562622019421854719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.477 × 10⁹⁸(99-digit number)

14779025984486582685…65562622019421854721

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

2.955 × 10⁹⁸(99-digit number)

29558051968973165371…31125244038843709439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.955 × 10⁹⁸(99-digit number)

29558051968973165371…31125244038843709441

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

5.911 × 10⁹⁸(99-digit number)

59116103937946330743…62250488077687418879

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