Block #177,617

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/23/2013, 7:21:52 PM · Difficulty 9.8646 · 6,618,527 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

04e65a51c91c9594f489e434a18336206a9a8f7a45485a1de05bbb9b801787cf

View on Chainz ↗

Height

#177,617

Difficulty

9.864624

Transactions

Size

2.56 KB

Version

Bits

09dd57ff

Nonce

95,080

Timestamp

9/23/2013, 7:21:52 PM

Confirmations

6,618,527

Mined by

⛏️ P2SHAGnfEuQMviRnevo4virZwtKFGqdhnYQhJx

Merkle Root

9495521c1b94f295bab090002508eb5ff53ea817d950be7e8fdd47a5760c3dd6

Transactions (4)

Coinbase1583b26fd999ec…3fad3acda69b20

1 in → 1 out10.3000 XPM109 B

AGnfEuQM…dhnYQhJx

80420669350fd9…ae6efa18b87357

2 in → 1 out131.9900 XPM341 B

AaiFSpvX…n3SS7r8o

8d344967b76ae0…46fbae5f536b39

3 in → 2 out400.0103 XPM521 B

AGZdrEaS…GCiZuko8 Af39crpC…YR8K5Xm3

9778f766c64b37…3f22a2fe0ad99a

10 in → 2 out102.8500 XPM1.52 KB

AVmZXCUr…VJdpT4Pm AYLNUwaf…4NGqw4pY

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.

8.239 × 10⁹³(94-digit number)

82393988524725503114…13464633528264518399

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

8.239 × 10⁹³(94-digit number)

82393988524725503114…13464633528264518399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.239 × 10⁹³(94-digit number)

82393988524725503114…13464633528264518401

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

1.647 × 10⁹⁴(95-digit number)

16478797704945100622…26929267056529036799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.647 × 10⁹⁴(95-digit number)

16478797704945100622…26929267056529036801

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

3.295 × 10⁹⁴(95-digit number)

32957595409890201245…53858534113058073599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.295 × 10⁹⁴(95-digit number)

32957595409890201245…53858534113058073601

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

6.591 × 10⁹⁴(95-digit number)

65915190819780402491…07717068226116147199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.591 × 10⁹⁴(95-digit number)

65915190819780402491…07717068226116147201

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

1.318 × 10⁹⁵(96-digit number)

13183038163956080498…15434136452232294399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.318 × 10⁹⁵(96-digit number)

13183038163956080498…15434136452232294401

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