Block #441,772

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/13/2014, 9:13:59 AM · Difficulty 10.3486 · 6,372,249 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

76d17891de6146e96ad61c56637269e5a54dc8c84c6200548b2b6317cd88772b

View on Chainz ↗

Height

#441,772

Difficulty

10.348634

Transactions

Size

1.53 KB

Version

Bits

0a594017

Nonce

6,607

Timestamp

3/13/2014, 9:13:59 AM

Confirmations

6,372,249

Mined by

⛏️ aS!vAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

ad4ea8a5c4af546285ec0df416e2f02c0715d53978187fe72d97ce989a9bf55d

Transactions (2)

Coinbase7395f4490872b1…8cc1172477fe13

1 in → 23 out9.3200 XPM844 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

a5d516b8bc73e5…80c8e7b874cc14

4 in → 1 out12.1323 XPM635 B

AY95xaay…JK8QuFZP

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.

7.091 × 10⁹⁴(95-digit number)

70918292730566227097…39629781331813007399

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

7.091 × 10⁹⁴(95-digit number)

70918292730566227097…39629781331813007399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.091 × 10⁹⁴(95-digit number)

70918292730566227097…39629781331813007401

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

1.418 × 10⁹⁵(96-digit number)

14183658546113245419…79259562663626014799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.418 × 10⁹⁵(96-digit number)

14183658546113245419…79259562663626014801

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

2.836 × 10⁹⁵(96-digit number)

28367317092226490838…58519125327252029599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.836 × 10⁹⁵(96-digit number)

28367317092226490838…58519125327252029601

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

5.673 × 10⁹⁵(96-digit number)

56734634184452981677…17038250654504059199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.673 × 10⁹⁵(96-digit number)

56734634184452981677…17038250654504059201

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

1.134 × 10⁹⁶(97-digit number)

11346926836890596335…34076501309008118399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.134 × 10⁹⁶(97-digit number)

11346926836890596335…34076501309008118401

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 #441,772

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