Block #922,409

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 11:07:43 AM · Difficulty 10.9155 · 5,876,560 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

23abb6cf3bfcda62cacdc31822a7f9df119fc1a61e12bd8e5592bbc290dde894

View on Chainz ↗

Height

#922,409

Difficulty

10.915458

Transactions

Size

115.95 KB

Version

Bits

0aea5b74

Nonce

683,579,264

Timestamp

2/4/2015, 11:07:43 AM

Confirmations

5,876,560

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

2cdefbae8319e29d07f0b42abd121b0210bc53d110fd4e1f2b053dc43dae5c60

Transactions (5)

Coinbase970229b07f71b8…3e9d78c406bd53

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

7ad817945ede41…e5acbe243685af

200 in → 1 out964.6544 XPM28.94 KB

AKuP4XsJ…owbodNxQ

dcf0ae5bc639f3…e814def65a80cd

200 in → 1 out1017.1450 XPM28.93 KB

AKuP4XsJ…owbodNxQ

f20da307bffe18…710a11a5fef97c

200 in → 1 out955.8844 XPM28.94 KB

AKuP4XsJ…owbodNxQ

3eb2a2831430d7…5e29fb8effac31

200 in → 1 out1117.5118 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.

2.809 × 10⁹⁵(96-digit number)

28090771587741157683…36058585598681309119

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

2.809 × 10⁹⁵(96-digit number)

28090771587741157683…36058585598681309119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.809 × 10⁹⁵(96-digit number)

28090771587741157683…36058585598681309121

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

5.618 × 10⁹⁵(96-digit number)

56181543175482315367…72117171197362618239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.618 × 10⁹⁵(96-digit number)

56181543175482315367…72117171197362618241

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

1.123 × 10⁹⁶(97-digit number)

11236308635096463073…44234342394725236479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.123 × 10⁹⁶(97-digit number)

11236308635096463073…44234342394725236481

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

2.247 × 10⁹⁶(97-digit number)

22472617270192926147…88468684789450472959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.247 × 10⁹⁶(97-digit number)

22472617270192926147…88468684789450472961

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

4.494 × 10⁹⁶(97-digit number)

44945234540385852294…76937369578900945919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.494 × 10⁹⁶(97-digit number)

44945234540385852294…76937369578900945921

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