Block #1,062,825

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/17/2015, 4:00:03 AM · Difficulty 10.7294 · 5,744,041 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d21e91e17cc7324a1daecf590fb221ad505cdd235028ceed7b58fc4be4a6a8de

View on Chainz ↗

Height

#1,062,825

Difficulty

10.729360

Transactions

Size

1.01 KB

Version

Bits

0abab75e

Nonce

309,959,465

Timestamp

5/17/2015, 4:00:03 AM

Confirmations

5,744,041

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b0cf9594e8aa6d7f12bde5656bcce9faebf7793f43ff88eba03706f66265c3a7

Transactions (4)

Coinbase808af058c00f72…c9d6d854ef4859

1 in → 1 out8.7000 XPM116 B

ANSXnLY2…Sd25TjkD

59c980814d4360…e44d36d8b46cc1

1 in → 2 out8.6600 XPM226 B

Af3aPj7K…cnGd5dnY Ac1jcr2o…UGtW3L48

038d39bafaa8de…8f0e19931201b7

2 in → 2 out11.4134 XPM376 B

ATo8D213…FnUe2HYb AXJGG9Ad…NytxiUD2

c047da683a526a…ef60057b82bc6f

1 in → 2 out6.2723 XPM227 B

ANz9RpaQ…LTt5oWBj ATzwV7X8…ProCkZBq

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.

1.935 × 10⁹⁷(98-digit number)

19358777185545447466…87232034928468991999

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

1.935 × 10⁹⁷(98-digit number)

19358777185545447466…87232034928468991999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.935 × 10⁹⁷(98-digit number)

19358777185545447466…87232034928468992001

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

3.871 × 10⁹⁷(98-digit number)

38717554371090894933…74464069856937983999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.871 × 10⁹⁷(98-digit number)

38717554371090894933…74464069856937984001

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

7.743 × 10⁹⁷(98-digit number)

77435108742181789867…48928139713875967999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.743 × 10⁹⁷(98-digit number)

77435108742181789867…48928139713875968001

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

1.548 × 10⁹⁸(99-digit number)

15487021748436357973…97856279427751935999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.548 × 10⁹⁸(99-digit number)

15487021748436357973…97856279427751936001

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

3.097 × 10⁹⁸(99-digit number)

30974043496872715947…95712558855503871999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.097 × 10⁹⁸(99-digit number)

30974043496872715947…95712558855503872001

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 #1,062,825

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