Block #1,051,972

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/9/2015, 1:57:50 PM · Difficulty 10.7325 · 5,757,150 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f815a4041c862c6b511b1eddca291dd94e15aa1e890408493a4875b7109e3be4

View on Chainz ↗

Height

#1,051,972

Difficulty

10.732542

Transactions

Size

660 B

Version

Bits

0abb87db

Nonce

491,511,349

Timestamp

5/9/2015, 1:57:50 PM

Confirmations

5,757,150

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

4138ae78a64462518a685555d6a701b294281ca6903ab32b762b136a8de3ad6c

Transactions (3)

Coinbase699cc54f90d96e…4b64b89d66b49b

1 in → 1 out8.6900 XPM116 B

ANSXnLY2…Sd25TjkD

83ffd35c8338ce…aaacc859bf6f06

1 in → 2 out8.6100 XPM225 B

AHmcchxr…vBbydp5n AJSSPwNG…jHwjfjbw

53ae60430d6f74…9241bc677ee4fc

1 in → 2 out2.6473 XPM227 B

AWQz7RrF…BszTBRNv AbvPGdpW…nARb1BE3

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.

8.162 × 10⁹⁸(99-digit number)

81622052819527094560…30953306083911598079

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

8.162 × 10⁹⁸(99-digit number)

81622052819527094560…30953306083911598079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.162 × 10⁹⁸(99-digit number)

81622052819527094560…30953306083911598081

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

1.632 × 10⁹⁹(100-digit number)

16324410563905418912…61906612167823196159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.632 × 10⁹⁹(100-digit number)

16324410563905418912…61906612167823196161

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

3.264 × 10⁹⁹(100-digit number)

32648821127810837824…23813224335646392319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.264 × 10⁹⁹(100-digit number)

32648821127810837824…23813224335646392321

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

6.529 × 10⁹⁹(100-digit number)

65297642255621675648…47626448671292784639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.529 × 10⁹⁹(100-digit number)

65297642255621675648…47626448671292784641

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

1.305 × 10¹⁰⁰(101-digit number)

13059528451124335129…95252897342585569279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.305 × 10¹⁰⁰(101-digit number)

13059528451124335129…95252897342585569281

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 #1,051,972

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