Block #922,296

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 8:56:28 AM · Difficulty 10.9158 · 5,870,758 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

27c040df3290fba4571577f812aa9b06757f19c5aae907a4335e840891741ecd

View on Chainz ↗

Height

#922,296

Difficulty

10.915756

Transactions

Size

115.98 KB

Version

Bits

0aea6efa

Nonce

127,342,454

Timestamp

2/4/2015, 8:56:28 AM

Confirmations

5,870,758

Merkle Root

1f83f9da30467c03c5a82c9217420169bfb01d9ba3d31379c7205ea88febe6f0

Transactions (5)

Coinbase16ae312ac5089b…ada269c932607a

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

05184d24135235…9270d9fe67a014

200 in → 1 out1138.1150 XPM28.95 KB

AKuP4XsJ…owbodNxQ

45bd038801d2e3…357e883bc1f05b

200 in → 1 out1029.9981 XPM28.94 KB

AKuP4XsJ…owbodNxQ

76cca899452e05…788f896c1e2370

200 in → 1 out929.1451 XPM28.94 KB

AKuP4XsJ…owbodNxQ

a66451d8054988…30a8a9041be5cb

200 in → 1 out1100.8166 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.

4.476 × 10⁹⁹(100-digit number)

44766941987583702498…63515383151239987199

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

4.476 × 10⁹⁹(100-digit number)

44766941987583702498…63515383151239987199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.476 × 10⁹⁹(100-digit number)

44766941987583702498…63515383151239987201

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

8.953 × 10⁹⁹(100-digit number)

89533883975167404997…27030766302479974399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.953 × 10⁹⁹(100-digit number)

89533883975167404997…27030766302479974401

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

1.790 × 10¹⁰⁰(101-digit number)

17906776795033480999…54061532604959948799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.790 × 10¹⁰⁰(101-digit number)

17906776795033480999…54061532604959948801

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

3.581 × 10¹⁰⁰(101-digit number)

35813553590066961999…08123065209919897599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.581 × 10¹⁰⁰(101-digit number)

35813553590066961999…08123065209919897601

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

7.162 × 10¹⁰⁰(101-digit number)

71627107180133923998…16246130419839795199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.162 × 10¹⁰⁰(101-digit number)

71627107180133923998…16246130419839795201

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