Block #170,120

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/18/2013, 1:02:50 PM · Difficulty 9.8660 · 6,643,958 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5c3bae85e5b956cd37b5c0f12e467723704c4b747d6314c377de062eb88880f3

View on Chainz ↗

Height

#170,120

Difficulty

9.866050

Transactions

Size

1.52 KB

Version

Bits

09ddb570

Nonce

17,491

Timestamp

9/18/2013, 1:02:50 PM

Confirmations

6,643,958

Mined by

⛏️ P2SHAdSpk7UpcXM5ifMcLQJphzWNCiZMGs2B2Y

Merkle Root

06f72158c33a31a91296cd9e775351fe5b264aa4a632f675a875c43ade807c9b

Transactions (4)

Coinbasee4b542585fe795…9c85ddf2026f09

1 in → 1 out10.2900 XPM109 B

AdSpk7Up…ZMGs2B2Y

c198a5905f281b…808ac2b7b53f5a

3 in → 1 out30.9600 XPM386 B

AMF6scky…ugQApVzx

cc51b220615873…762f3f2ac49d7a

5 in → 2 out51.2800 XPM819 B

AHUgkEqf…b9YEDMVk AeC9eoyd…eGa9xvQX

2a3225e52bd115…c0df389d07089d

1 in → 1 out10.2400 XPM158 B

AcWWWPc4…NKmGSdQs

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.

2.297 × 10⁹¹(92-digit number)

22970516492351737176…78815622284579061059

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

2.297 × 10⁹¹(92-digit number)

22970516492351737176…78815622284579061059

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.297 × 10⁹¹(92-digit number)

22970516492351737176…78815622284579061061

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

4.594 × 10⁹¹(92-digit number)

45941032984703474353…57631244569158122119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.594 × 10⁹¹(92-digit number)

45941032984703474353…57631244569158122121

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

9.188 × 10⁹¹(92-digit number)

91882065969406948706…15262489138316244239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.188 × 10⁹¹(92-digit number)

91882065969406948706…15262489138316244241

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

1.837 × 10⁹²(93-digit number)

18376413193881389741…30524978276632488479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.837 × 10⁹²(93-digit number)

18376413193881389741…30524978276632488481

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

3.675 × 10⁹²(93-digit number)

36752826387762779482…61049956553264976959

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

Block #170,120

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