Block #727,391

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/18/2014, 12:15:15 PM · Difficulty 10.9619 · 6,072,068 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cd51d88482457c8070e236651598d9c810dc4d23e1cddba01a9f06a60045f97e

View on Chainz ↗

Height

#727,391

Difficulty

10.961941

Transactions

Size

956 B

Version

Bits

0af641c3

Nonce

2,018,587,523

Timestamp

9/18/2014, 12:15:15 PM

Confirmations

6,072,068

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c293b9c5fc12a8d2f08062f0cdb2ec3a55115aabe68452e2c922b28dd35a54d6

Transactions (3)

Coinbase86b25eec1173e5…43a9def5192f16

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

d6c95ff18de0f9…f205063c1596b4

2 in → 2 out1.0120 XPM375 B

Aa87tsJj…E3Fbccuc ARMmjyvz…4PLUTMJK

ec49d38f1ee9ae…9f96e93134ca75

2 in → 2 out10.6982 XPM374 B

Aaf8XL56…tMsc49uq ARVNpN7t…qWforj8h

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.

1.736 × 10⁹⁸(99-digit number)

17361355588894176136…25322796065773465599

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

1.736 × 10⁹⁸(99-digit number)

17361355588894176136…25322796065773465599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.736 × 10⁹⁸(99-digit number)

17361355588894176136…25322796065773465601

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

3.472 × 10⁹⁸(99-digit number)

34722711177788352272…50645592131546931199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.472 × 10⁹⁸(99-digit number)

34722711177788352272…50645592131546931201

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

6.944 × 10⁹⁸(99-digit number)

69445422355576704545…01291184263093862399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.944 × 10⁹⁸(99-digit number)

69445422355576704545…01291184263093862401

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

1.388 × 10⁹⁹(100-digit number)

13889084471115340909…02582368526187724799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.388 × 10⁹⁹(100-digit number)

13889084471115340909…02582368526187724801

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

2.777 × 10⁹⁹(100-digit number)

27778168942230681818…05164737052375449599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.777 × 10⁹⁹(100-digit number)

27778168942230681818…05164737052375449601

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