Block #2,115,869

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/14/2017, 1:22:27 PM · Difficulty 10.9028 · 4,717,921 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b5d46d98e598014f817228a9f51cb19d66c7638b99de86c2c5df3e62b4abc088

View on Chainz ↗

Height

#2,115,869

Difficulty

10.902776

Transactions

Size

428 B

Version

Bits

0ae71c58

Nonce

375,854,190

Timestamp

5/14/2017, 1:22:27 PM

Confirmations

4,717,921

Mined by

⛏️ P2SHAVH9SSjnJAEXVn2aKitjPVAuSjyrGae47t

Merkle Root

9094beb8feb46b206677564907f2598a40e436f20e78069106714fc4a490af94

Transactions (2)

Coinbase2e32a912c1e6da…5dbcd0f343d372

1 in → 1 out8.4100 XPM110 B

AVH9SSjn…yrGae47t

a28c7ef9a6d0f2…7c60105636b555

1 in → 2 out111673.5543 XPM227 B

ATNNwPCV…id21vw5x AKeebDSB…gu7ivvBp

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.

2.575 × 10⁹⁶(97-digit number)

25750380999019000252…76930386982733823999

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

2.575 × 10⁹⁶(97-digit number)

25750380999019000252…76930386982733823999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.575 × 10⁹⁶(97-digit number)

25750380999019000252…76930386982733824001

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

5.150 × 10⁹⁶(97-digit number)

51500761998038000504…53860773965467647999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.150 × 10⁹⁶(97-digit number)

51500761998038000504…53860773965467648001

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

1.030 × 10⁹⁷(98-digit number)

10300152399607600100…07721547930935295999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.030 × 10⁹⁷(98-digit number)

10300152399607600100…07721547930935296001

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

2.060 × 10⁹⁷(98-digit number)

20600304799215200201…15443095861870591999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.060 × 10⁹⁷(98-digit number)

20600304799215200201…15443095861870592001

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

4.120 × 10⁹⁷(98-digit number)

41200609598430400403…30886191723741183999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.120 × 10⁹⁷(98-digit number)

41200609598430400403…30886191723741184001

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 #2,115,869

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