Block #1,455,357

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/14/2016, 1:22:28 AM · Difficulty 10.7313 · 5,369,774 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a481c460233e9659e9e0a7b49348cff50df71d62b32959b3326c89ca00c6c6c1

View on Chainz ↗

Height

#1,455,357

Difficulty

10.731272

Transactions

Size

6.17 KB

Version

Bits

0abb34a6

Nonce

224,697,102

Timestamp

2/14/2016, 1:22:28 AM

Confirmations

5,369,774

Mined by

⛏️ P2SHAZ47NeURdewxK7JSp3nbgzJP6VWKVTnaX4

Merkle Root

71a3fc04b61ea6b34c687bdf74a20bc68fa874e5898a41110090709b341be9df

Transactions (4)

Coinbaseb320951c426a6a…6b9befdb3c1fc4

1 in → 1 out8.7400 XPM110 B

AZ47NeUR…WKVTnaX4

e68d69ae874cc2…523faaf38a6764

1 in → 51 out79.7133 XPM1.85 KB

AJXQ8632…qnKSnpkP AZ7e8o5N…6CwHP23z AT2YG1xt…pgrnT3Xe AcKQbxHx…GU5ytzuw AYNMyuCc…csbpZzVF

58cf8677bb4bf8…a2d6e3349b8bda

1 in → 51 out19.1847 XPM1.85 KB

AGQJsEPX…iyhd2Ujp AGnP9URo…KpVnR3hk AdLbencU…ETVmgdUu AKyzMmZh…X7GBPREH AJ5u3Hok…zj9uSzXD

1d09499e424ccc…f52a81b8546d06

4 in → 51 out1.1890 XPM2.28 KB

ASWrAqET…TdVD9rjD AMmtwDhT…QcsJ1n5D AKJTDxwW…HcrWTrPn APcG6q72…yjVvWXyb AT5f148F…gcAARTzJ

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.

4.432 × 10⁹⁵(96-digit number)

44328419107461640232…51876866628298443519

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

4.432 × 10⁹⁵(96-digit number)

44328419107461640232…51876866628298443519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.432 × 10⁹⁵(96-digit number)

44328419107461640232…51876866628298443521

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

8.865 × 10⁹⁵(96-digit number)

88656838214923280465…03753733256596887039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.865 × 10⁹⁵(96-digit number)

88656838214923280465…03753733256596887041

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

1.773 × 10⁹⁶(97-digit number)

17731367642984656093…07507466513193774079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.773 × 10⁹⁶(97-digit number)

17731367642984656093…07507466513193774081

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

3.546 × 10⁹⁶(97-digit number)

35462735285969312186…15014933026387548159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.546 × 10⁹⁶(97-digit number)

35462735285969312186…15014933026387548161

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

7.092 × 10⁹⁶(97-digit number)

70925470571938624372…30029866052775096319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.092 × 10⁹⁶(97-digit number)

70925470571938624372…30029866052775096321

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 #1,455,357

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