Block #222,800

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/22/2013, 11:50:59 AM · Difficulty 9.9395 · 6,572,002 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

abea291c09afa7348869f0bb360f86c5d3c5fd52ea345a7a19daf2d7f033c4dd

View on Chainz ↗

Height

#222,800

Difficulty

9.939510

Transactions

Size

88.41 KB

Version

Bits

09f083c0

Nonce

255,795

Timestamp

10/22/2013, 11:50:59 AM

Confirmations

6,572,002

Mined by

⛏️ P2SHAaXb6LdzMFohbBjmNyta5dnWNNXefG91jF

Merkle Root

0c09d8964fd0ba8243bfaea276eba59a050b6fad38dd52c6828fc1c8b40e82b3

Transactions (4)

Coinbasec3b72650f7ef9f…39893d1c884043

1 in → 1 out11.0300 XPM100 B

AaXb6Ldz…XefG91jF

50f41c17360d36…d7a2d1d4f880de

3 in → 2 out300.0146 XPM523 B

AQ8ZTdvi…VSj97Mto ATDg1wpK…dc5kwZ3e

ac0b81e35bea17…018fd9e1b79ac7

3 in → 2 out300.0152 XPM523 B

AW3oqdog…1qjNKMmh AJ9PGs5b…uCussLha

c97ca9a9a19409…ef35cfaba07b71

603 in → 2 out174.0100 XPM87.20 KB

AUgrjese…CzLS2itw AN8nUzff…YcDfRDQ2

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.

1.621 × 10⁹⁷(98-digit number)

16217499553863476165…84299740679097937919

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

1.621 × 10⁹⁷(98-digit number)

16217499553863476165…84299740679097937919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.621 × 10⁹⁷(98-digit number)

16217499553863476165…84299740679097937921

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

3.243 × 10⁹⁷(98-digit number)

32434999107726952330…68599481358195875839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.243 × 10⁹⁷(98-digit number)

32434999107726952330…68599481358195875841

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

6.486 × 10⁹⁷(98-digit number)

64869998215453904660…37198962716391751679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.486 × 10⁹⁷(98-digit number)

64869998215453904660…37198962716391751681

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

1.297 × 10⁹⁸(99-digit number)

12973999643090780932…74397925432783503359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.297 × 10⁹⁸(99-digit number)

12973999643090780932…74397925432783503361

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

2.594 × 10⁹⁸(99-digit number)

25947999286181561864…48795850865567006719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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