Block #2,262,865

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/22/2017, 9:39:09 AM · Difficulty 10.9521 · 4,578,226 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ac456c4c9417a3fcc61032e647279c1403a071d4b23e592e7fe0fd0af7d072f1

View on Chainz ↗

Height

#2,262,865

Difficulty

10.952094

Transactions

Size

880 B

Version

Bits

0af3bc6f

Nonce

666,459,760

Timestamp

8/22/2017, 9:39:09 AM

Confirmations

4,578,226

Mined by

⛏️ P2SHANuLxaSfgqShkVQgfA5wYV9dddBxbCQC5g

Merkle Root

2b8f3ec3803439aec35f28125964f0dec05221d1bf072f9c4f023267d9c7849b

Transactions (4)

Coinbase3529b9bd34ef02…b3ad1fd80c896f

1 in → 1 out8.3500 XPM110 B

ANuLxaSf…BxbCQC5g

f844120f23709e…b78941cb0bed67

1 in → 2 out3466.2344 XPM225 B

AViBaKwf…3Xk3qwK8 AL2Wo4Bd…VRKqxFTT

377ce9f960a559…45302101f823f7

1 in → 2 out1166.9435 XPM227 B

AKk5vUA3…gfC1xm54 AVQMAjiZ…hK66B5EE

0fb57f24e51246…c5c45b9b0f90f8

1 in → 2 out435.8244 XPM227 B

AcKyL6X5…CPAuZdVc AKhRJWxX…BWSHbHap

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.

6.974 × 10⁹⁷(98-digit number)

69747011895340064017…88382270655723151359

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

6.974 × 10⁹⁷(98-digit number)

69747011895340064017…88382270655723151359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.974 × 10⁹⁷(98-digit number)

69747011895340064017…88382270655723151361

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

1.394 × 10⁹⁸(99-digit number)

13949402379068012803…76764541311446302719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.394 × 10⁹⁸(99-digit number)

13949402379068012803…76764541311446302721

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

2.789 × 10⁹⁸(99-digit number)

27898804758136025606…53529082622892605439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.789 × 10⁹⁸(99-digit number)

27898804758136025606…53529082622892605441

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

5.579 × 10⁹⁸(99-digit number)

55797609516272051213…07058165245785210879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.579 × 10⁹⁸(99-digit number)

55797609516272051213…07058165245785210881

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

1.115 × 10⁹⁹(100-digit number)

11159521903254410242…14116330491570421759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.115 × 10⁹⁹(100-digit number)

11159521903254410242…14116330491570421761

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 #2,262,865

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