Block #2,236,807

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/4/2017, 3:37:17 PM · Difficulty 10.9463 · 4,606,117 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

890d5901ccd8c7f7238d70ee9a1244cde94a01d075867c21dc21122a4a2db4b6

View on Chainz ↗

Height

#2,236,807

Difficulty

10.946326

Transactions

Size

1.69 KB

Version

Bits

0af24267

Nonce

15,031,445

Timestamp

8/4/2017, 3:37:17 PM

Confirmations

4,606,117

Mined by

⛏️ P2SHARB4Ja3T8PpA656kvGLeK9XMP4kGQL4fFm

Merkle Root

f197697fedfdf4df4f07025e6719530c0a80a4cd110127baca0cd9638a5177e6

Transactions (4)

Coinbase9ec92e1b1cdf9d…00f9bd246dd4bd

1 in → 1 out8.3600 XPM109 B

ARB4Ja3T…kGQL4fFm

7f46e53d09e238…b7eef2e26f137f

2 in → 1 out1019.9900 XPM342 B

AcxhUhX6…N8N8w2tm

72c643d30287f2…9dbd1bfc719fe4

5 in → 2 out2970.0137 XPM819 B

AT2bsHQJ…tAPqT8ME AYr6cjSv…r9xr8tZy

d35fd52d975919…962470a4ab9536

2 in → 2 out643.4900 XPM374 B

AesaHg9U…6tjRExna AWjMKgt3…SigzuF2o

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.

6.600 × 10⁹³(94-digit number)

66001281649307569663…99801983323387781719

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

6.600 × 10⁹³(94-digit number)

66001281649307569663…99801983323387781719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.600 × 10⁹³(94-digit number)

66001281649307569663…99801983323387781721

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

1.320 × 10⁹⁴(95-digit number)

13200256329861513932…99603966646775563439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.320 × 10⁹⁴(95-digit number)

13200256329861513932…99603966646775563441

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

2.640 × 10⁹⁴(95-digit number)

26400512659723027865…99207933293551126879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.640 × 10⁹⁴(95-digit number)

26400512659723027865…99207933293551126881

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

5.280 × 10⁹⁴(95-digit number)

52801025319446055731…98415866587102253759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.280 × 10⁹⁴(95-digit number)

52801025319446055731…98415866587102253761

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

1.056 × 10⁹⁵(96-digit number)

10560205063889211146…96831733174204507519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.056 × 10⁹⁵(96-digit number)

10560205063889211146…96831733174204507521

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 #2,236,807

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