Block #2,270,316

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/27/2017, 1:00:12 PM · Difficulty 10.9528 · 4,561,233 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1b769097cc96569b544f33cfbe8aba21fc3f13af814640b6c96d7df2c76d731c

View on Chainz ↗

Height

#2,270,316

Difficulty

10.952781

Transactions

Size

2.81 KB

Version

Bits

0af3e96f

Nonce

376,458,807

Timestamp

8/27/2017, 1:00:12 PM

Confirmations

4,561,233

Mined by

⛏️ P2SHAT4Txx6WgrWnrRgwvf6cRrKsxhAGNxKnLu

Merkle Root

f6a029df2978b0721a607c227cc82212d94aef4dce878b2f5710c12888ca36e7

Transactions (5)

Coinbase4ced60c94d5bed…18d351ed4460aa

1 in → 1 out8.3600 XPM110 B

AT4Txx6W…AGNxKnLu

aa5d8cf9743f69…3d7481d490b24f

3 in → 2 out2970.0380 XPM523 B

AMKbiSFr…3bdeNkja AeTKdJzo…EdMmwZXt

8f16a180296815…6acdfa1f1f03db

5 in → 2 out2970.0300 XPM817 B

AXadmJLN…q5VMTCtt AMKbiSFr…3bdeNkja

bfc1c3e3b10da8…9f46c1ccdfbfbe

4 in → 2 out2970.0229 XPM669 B

AMKbiSFr…3bdeNkja ALziFiDf…zMZR6ctW

848fd2f443394a…b954b7219d22ee

4 in → 2 out2970.0300 XPM669 B

AJQs5Lju…mb6Axzn8 AMKbiSFr…3bdeNkja

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.

4.049 × 10⁹⁸(99-digit number)

40494584012723865661…92938593547585781759

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

4.049 × 10⁹⁸(99-digit number)

40494584012723865661…92938593547585781759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.049 × 10⁹⁸(99-digit number)

40494584012723865661…92938593547585781761

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

8.098 × 10⁹⁸(99-digit number)

80989168025447731323…85877187095171563519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.098 × 10⁹⁸(99-digit number)

80989168025447731323…85877187095171563521

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

1.619 × 10⁹⁹(100-digit number)

16197833605089546264…71754374190343127039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.619 × 10⁹⁹(100-digit number)

16197833605089546264…71754374190343127041

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

3.239 × 10⁹⁹(100-digit number)

32395667210179092529…43508748380686254079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.239 × 10⁹⁹(100-digit number)

32395667210179092529…43508748380686254081

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

6.479 × 10⁹⁹(100-digit number)

64791334420358185058…87017496761372508159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.479 × 10⁹⁹(100-digit number)

64791334420358185058…87017496761372508161

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 #2,270,316

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