Block #2,120,032

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/17/2017, 2:39:35 AM · Difficulty 10.9118 · 4,721,751 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

524e85ed57b4aee6c22b43e17a6e093ca2688753e3f9f303935bc4eb36aa9388

View on Chainz ↗

Height

#2,120,032

Difficulty

10.911817

Transactions

Size

651 B

Version

Bits

0ae96cdc

Nonce

187,527,595

Timestamp

5/17/2017, 2:39:35 AM

Confirmations

4,721,751

Mined by

⛏️ P2SHAb9GLTSFTTJoN4S5rusSg1EY6kk1xa7wkr

Merkle Root

40aa42abf0fe9d1baf83757812b3701c81a948d671abd7c704072e8c4cc33be4

Transactions (3)

Coinbaseaf1069c392e95b…a75a0764bd4eec

1 in → 1 out8.4100 XPM110 B

Ab9GLTSF…k1xa7wkr

e6384c75e5cd74…71771e0dd74cce

1 in → 2 out876.1194 XPM225 B

AQqE8W9M…N7Z7sQgo ARCmBDoY…gArebFoK

b722299a26a744…bca4a83d948f8e

1 in → 2 out138.5900 XPM225 B

AbqXRqrX…93pFH86f AKNPibZF…ojhmrgzG

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.

2.364 × 10⁹⁶(97-digit number)

23641249114790691466…75448559688106734079

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

2.364 × 10⁹⁶(97-digit number)

23641249114790691466…75448559688106734079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.364 × 10⁹⁶(97-digit number)

23641249114790691466…75448559688106734081

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

4.728 × 10⁹⁶(97-digit number)

47282498229581382933…50897119376213468159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.728 × 10⁹⁶(97-digit number)

47282498229581382933…50897119376213468161

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

9.456 × 10⁹⁶(97-digit number)

94564996459162765866…01794238752426936319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.456 × 10⁹⁶(97-digit number)

94564996459162765866…01794238752426936321

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

1.891 × 10⁹⁷(98-digit number)

18912999291832553173…03588477504853872639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.891 × 10⁹⁷(98-digit number)

18912999291832553173…03588477504853872641

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

3.782 × 10⁹⁷(98-digit number)

37825998583665106346…07176955009707745279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.782 × 10⁹⁷(98-digit number)

37825998583665106346…07176955009707745281

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 #2,120,032

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