Block #2,650,099

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/5/2018, 6:51:50 PM · Difficulty 11.7591 · 4,195,090 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7b756f3b19b3d6516bd45b2d2807f9512e8edbfa61bdf6c8252ab7a977841bdf

View on Chainz ↗

Height

#2,650,099

Difficulty

11.759096

Transactions

Size

722 B

Version

Bits

0bc25419

Nonce

518,725,213

Timestamp

5/5/2018, 6:51:50 PM

Confirmations

4,195,090

Mined by

⛏️ P2SHAKP9soodN8jQryVNVvn2G4j1F8SVRX36mZ

Merkle Root

9f954e6b9ae80f38408a27197df20e3a7aa4121abeaa575df572621ffdf68292

Transactions (2)

Coinbase37a8071ac8a973…5bfe508b2ba339

1 in → 1 out7.2300 XPM110 B

AKP9sood…SVRX36mZ

8a59ab7ba2f21c…c07d8c3d0a1459

3 in → 2 out160.5121 XPM521 B

ARTGxeAc…WmRAvHDa AM9tVVrX…2oZL6aoo

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.

2.877 × 10⁹⁶(97-digit number)

28777670778472088243…74615546828841692159

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

2.877 × 10⁹⁶(97-digit number)

28777670778472088243…74615546828841692159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.877 × 10⁹⁶(97-digit number)

28777670778472088243…74615546828841692161

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

5.755 × 10⁹⁶(97-digit number)

57555341556944176487…49231093657683384319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.755 × 10⁹⁶(97-digit number)

57555341556944176487…49231093657683384321

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

1.151 × 10⁹⁷(98-digit number)

11511068311388835297…98462187315366768639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.151 × 10⁹⁷(98-digit number)

11511068311388835297…98462187315366768641

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

2.302 × 10⁹⁷(98-digit number)

23022136622777670594…96924374630733537279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.302 × 10⁹⁷(98-digit number)

23022136622777670594…96924374630733537281

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

4.604 × 10⁹⁷(98-digit number)

46044273245555341189…93848749261467074559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.604 × 10⁹⁷(98-digit number)

46044273245555341189…93848749261467074561

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

9.208 × 10⁹⁷(98-digit number)

92088546491110682379…87697498522934149119

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 #2,650,099

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