Block #2,140,367

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/1/2017, 10:42:24 AM · Difficulty 10.8762 · 4,702,477 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ef6684c6ef5b0f55f0439ac3f44c6aa8ceb1d08a5bb7ed2db0c4a2382225407b

View on Chainz ↗

Height

#2,140,367

Difficulty

10.876186

Transactions

Size

649 B

Version

Bits

0ae04db4

Nonce

249,033,096

Timestamp

6/1/2017, 10:42:24 AM

Confirmations

4,702,477

Mined by

⛏️ P2SHAK8Liw3fmAHznFTfRskFTtovoxPQebsEKS

Merkle Root

92d8406f057f8ba73edc46922cb15cc3d4372161c094de31e8144239bbe1097d

Transactions (3)

Coinbase5e7251067f6d29…c55afde948ea10

1 in → 1 out8.4600 XPM109 B

AK8Liw3f…PQebsEKS

71962f221f853e…6c0c9c98df62d4

1 in → 2 out6730.6228 XPM225 B

AccqFsLE…FxQS1DH4 AeSSZYbb…Xg6HCQn2

33429f7d77a227…9ee47195e221ed

1 in → 2 out1102.5619 XPM226 B

AZopCVfr…rmQ4Gwdh AS1FQFPb…EZ1ibmQL

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.

1.214 × 10⁹³(94-digit number)

12141327166146217797…70746060537518740479

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

1.214 × 10⁹³(94-digit number)

12141327166146217797…70746060537518740479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.214 × 10⁹³(94-digit number)

12141327166146217797…70746060537518740481

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

2.428 × 10⁹³(94-digit number)

24282654332292435594…41492121075037480959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.428 × 10⁹³(94-digit number)

24282654332292435594…41492121075037480961

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

4.856 × 10⁹³(94-digit number)

48565308664584871188…82984242150074961919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.856 × 10⁹³(94-digit number)

48565308664584871188…82984242150074961921

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

9.713 × 10⁹³(94-digit number)

97130617329169742377…65968484300149923839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.713 × 10⁹³(94-digit number)

97130617329169742377…65968484300149923841

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

1.942 × 10⁹⁴(95-digit number)

19426123465833948475…31936968600299847679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.942 × 10⁹⁴(95-digit number)

19426123465833948475…31936968600299847681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.885 × 10⁹⁴(95-digit number)

38852246931667896951…63873937200599695359

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,140,367

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