Block #1,733,185

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/25/2016, 6:02:56 AM · Difficulty 10.7206 · 5,093,721 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

81f417757bad0844b3552f2221c5086381b7f2f0a4dfb4e0867fd7dc52b4f933

View on Chainz ↗

Height

#1,733,185

Difficulty

10.720584

Transactions

Size

527 B

Version

Bits

0ab87832

Nonce

460,601,861

Timestamp

8/25/2016, 6:02:56 AM

Confirmations

5,093,721

Mined by

⛏️ P2SHAYDQ7hwBrpWeeNCnhvyMGW1TuRmdY36ctD

Merkle Root

65a5e0d8f0781fcd59683319605ec892c21daf08dd86d426b46d2c0e4352055e

Transactions (2)

Coinbasea35b2ab51a317c…7c156ce8c73ea3

1 in → 1 out8.7000 XPM109 B

AYDQ7hwB…mdY36ctD

587ebfaad6fe97…7723f6e22e6db2

1 in → 5 out43.2237 XPM328 B

AQNTXgq7…gxriqWEb AZR8nRhh…34hZuEiP AJhcBVpJ…KVQr3ZxC AVrH4oyR…wKS6vKz8 AbP1K5yZ…1ZsyRGqy

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.

5.195 × 10⁹⁵(96-digit number)

51953511929009342891…75919388818597103039

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

5.195 × 10⁹⁵(96-digit number)

51953511929009342891…75919388818597103039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.195 × 10⁹⁵(96-digit number)

51953511929009342891…75919388818597103041

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

1.039 × 10⁹⁶(97-digit number)

10390702385801868578…51838777637194206079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.039 × 10⁹⁶(97-digit number)

10390702385801868578…51838777637194206081

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

2.078 × 10⁹⁶(97-digit number)

20781404771603737156…03677555274388412159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.078 × 10⁹⁶(97-digit number)

20781404771603737156…03677555274388412161

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

4.156 × 10⁹⁶(97-digit number)

41562809543207474313…07355110548776824319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.156 × 10⁹⁶(97-digit number)

41562809543207474313…07355110548776824321

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

8.312 × 10⁹⁶(97-digit number)

83125619086414948627…14710221097553648639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.312 × 10⁹⁶(97-digit number)

83125619086414948627…14710221097553648641

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

Block #1,733,185

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