Block #2,829,400

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/7/2018, 11:41:18 PM · Difficulty 11.7123 · 4,015,925 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c5fdf7404ca35635bc375934e4f36b8ceca2a1e58313b9b82da3a9d98fcc0d62

View on Chainz ↗

Height

#2,829,400

Difficulty

11.712300

Transactions

Size

1018 B

Version

Bits

0bb6594e

Nonce

930,446,929

Timestamp

9/7/2018, 11:41:18 PM

Confirmations

4,015,925

Mined by

⛏️ P2SHAcLkEoLcNkThCjF71zNstLrxoZ6GAYdDnm

Merkle Root

64754115d822f01757bfa5c4cc41732425f489622cfc8703e6ef46374fe8bf60

Transactions (2)

Coinbase8ef7ab0653bfc2…4a2f1e4aa66ca1

1 in → 1 out7.2900 XPM109 B

AcLkEoLc…6GAYdDnm

5460acfc497b99…3c358e6219c942

5 in → 2 out109.6465 XPM818 B

AcMCyQKB…PqAVPFxo AKT7X3Ga…HtU3cDUA

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.

1.035 × 10⁹⁸(99-digit number)

10354594819495819857…69976379275432755199

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

1.035 × 10⁹⁸(99-digit number)

10354594819495819857…69976379275432755199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.035 × 10⁹⁸(99-digit number)

10354594819495819857…69976379275432755201

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

2.070 × 10⁹⁸(99-digit number)

20709189638991639715…39952758550865510399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.070 × 10⁹⁸(99-digit number)

20709189638991639715…39952758550865510401

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

4.141 × 10⁹⁸(99-digit number)

41418379277983279431…79905517101731020799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.141 × 10⁹⁸(99-digit number)

41418379277983279431…79905517101731020801

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

8.283 × 10⁹⁸(99-digit number)

82836758555966558863…59811034203462041599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.283 × 10⁹⁸(99-digit number)

82836758555966558863…59811034203462041601

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

1.656 × 10⁹⁹(100-digit number)

16567351711193311772…19622068406924083199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.656 × 10⁹⁹(100-digit number)

16567351711193311772…19622068406924083201

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

3.313 × 10⁹⁹(100-digit number)

33134703422386623545…39244136813848166399

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 #2,829,400

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