Block #2,699,723

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/10/2018, 3:37:20 PM · Difficulty 11.6422 · 4,142,805 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bf56fe0eb00170d6a59d2656dc1108b766fdf9828dcc830e577de917df065960

View on Chainz ↗

Height

#2,699,723

Difficulty

11.642216

Transactions

Size

878 B

Version

Bits

0ba46843

Nonce

674,652,749

Timestamp

6/10/2018, 3:37:20 PM

Confirmations

4,142,805

Mined by

⛏️ P2SHAcLZVLabjqQivkauqauXJ9oCPbt74qrisG

Merkle Root

58b64118fae121fc31f98f27c215f915b0048a5b0b1e124fd68ba7bda14ddf8f

Transactions (4)

Coinbase275fa89ff208f1…4899b5004370fa

1 in → 1 out7.4000 XPM110 B

AcLZVLab…t74qrisG

36b8ab81f50d4d…ece2f85da8c31f

1 in → 2 out489.9425 XPM226 B

AeFPzsec…hFVYg7Ng AQ4SNE95…v3WkCAHZ

1c3e02a38b06b5…fff1a210432762

1 in → 2 out391.8027 XPM225 B

AQdVsxd5…VfqjTzs2 AXzSvx5H…XuBaZeeK

483dffc6fc2bb4…5c31aa4cd66252

1 in → 2 out136.9205 XPM226 B

AT6syLbX…ndgNrNRH ANjMHAV4…ExqzwP3r

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.

1.087 × 10⁹⁶(97-digit number)

10877037164478110186…62428439955386695679

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

1.087 × 10⁹⁶(97-digit number)

10877037164478110186…62428439955386695679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.087 × 10⁹⁶(97-digit number)

10877037164478110186…62428439955386695681

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

2.175 × 10⁹⁶(97-digit number)

21754074328956220372…24856879910773391359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.175 × 10⁹⁶(97-digit number)

21754074328956220372…24856879910773391361

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

4.350 × 10⁹⁶(97-digit number)

43508148657912440744…49713759821546782719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.350 × 10⁹⁶(97-digit number)

43508148657912440744…49713759821546782721

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

8.701 × 10⁹⁶(97-digit number)

87016297315824881489…99427519643093565439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.701 × 10⁹⁶(97-digit number)

87016297315824881489…99427519643093565441

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

1.740 × 10⁹⁷(98-digit number)

17403259463164976297…98855039286187130879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.740 × 10⁹⁷(98-digit number)

17403259463164976297…98855039286187130881

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

3.480 × 10⁹⁷(98-digit number)

34806518926329952595…97710078572374261759

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 #2,699,723

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