Block #2,279,299

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/2/2017, 1:26:27 PM · Difficulty 10.9559 · 4,547,426 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f3abcd3915338fec7811615a9f5e3bb802e7885a105325198d6e4dc10bf89d1e

View on Chainz ↗

Height

#2,279,299

Difficulty

10.955928

Transactions

Size

73.86 KB

Version

Bits

0af4b7ab

Nonce

520,638,460

Timestamp

9/2/2017, 1:26:27 PM

Confirmations

4,547,426

Mined by

⛏️ P2SHAQ5e7zSZitGaKaGKAk9sJB4bDM2CxZKbDW

Merkle Root

ac7efaeda6aaec9ded5a7ca73e55871c9880877fa3a3397cb8cb0620deca47b2

Transactions (2)

Coinbasea180df7a695c3e…16a7ccba3c6e09

1 in → 1 out9.0800 XPM109 B

AQ5e7zSZ…2CxZKbDW

f542ddaef58ba1…de4b2211ee48c9

509 in → 2 out5700.0215 XPM73.67 KB

ATsGpLaK…6ivo8bfZ APzWDxfH…PYbF5nnE

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.

6.266 × 10⁹⁵(96-digit number)

62661250081498983288…80474465267689395199

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

6.266 × 10⁹⁵(96-digit number)

62661250081498983288…80474465267689395199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.266 × 10⁹⁵(96-digit number)

62661250081498983288…80474465267689395201

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

1.253 × 10⁹⁶(97-digit number)

12532250016299796657…60948930535378790399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.253 × 10⁹⁶(97-digit number)

12532250016299796657…60948930535378790401

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

2.506 × 10⁹⁶(97-digit number)

25064500032599593315…21897861070757580799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.506 × 10⁹⁶(97-digit number)

25064500032599593315…21897861070757580801

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

5.012 × 10⁹⁶(97-digit number)

50129000065199186630…43795722141515161599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.012 × 10⁹⁶(97-digit number)

50129000065199186630…43795722141515161601

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

1.002 × 10⁹⁷(98-digit number)

10025800013039837326…87591444283030323199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.002 × 10⁹⁷(98-digit number)

10025800013039837326…87591444283030323201

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 #2,279,299

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