Block #2,099,981

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/4/2017, 9:26:12 PM · Difficulty 10.8556 · 4,742,035 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

097a70cea792e950af6723ba5f9592db5fe1c31e86b5a1e301638afdaed09ae4

View on Chainz ↗

Height

#2,099,981

Difficulty

10.855601

Transactions

Size

40.25 KB

Version

Bits

0adb08a8

Nonce

668,054,063

Timestamp

5/4/2017, 9:26:12 PM

Confirmations

4,742,035

Mined by

⛏️ P2SHAKVZ4SkfVuGG49gfNS682ciALXYcNrwD7D

Merkle Root

945f18f12669b286a0e0999f565fa9b29c59ddcf605a04ddca38fd35968a60e3

Transactions (4)

Coinbased8d33ca6cdca23…f9fc5dce068d3a

1 in → 1 out8.8900 XPM110 B

AKVZ4Skf…YcNrwD7D

8a4f28e73e7f17…1e9e322c78a73f

119 in → 2 out1005.4100 XPM13.33 KB

AZyJg7WL…sEjxo2oo AKPDwVGe…ar4xwjSg

a7490a00ba5221…ee1b5d35b8a64d

119 in → 2 out1001.1052 XPM13.35 KB

AZyJg7WL…sEjxo2oo ALnXmCPh…ub5bNvkx

3c17ad22175310…d2dd0d0ba60bd3

119 in → 2 out1003.2721 XPM13.37 KB

AZyJg7WL…sEjxo2oo ActpVaHo…XLHAEnU8

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.

1.107 × 10⁹⁵(96-digit number)

11073842057874780278…57603088938802094079

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

1.107 × 10⁹⁵(96-digit number)

11073842057874780278…57603088938802094079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.107 × 10⁹⁵(96-digit number)

11073842057874780278…57603088938802094081

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

2.214 × 10⁹⁵(96-digit number)

22147684115749560556…15206177877604188159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.214 × 10⁹⁵(96-digit number)

22147684115749560556…15206177877604188161

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

4.429 × 10⁹⁵(96-digit number)

44295368231499121112…30412355755208376319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.429 × 10⁹⁵(96-digit number)

44295368231499121112…30412355755208376321

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

8.859 × 10⁹⁵(96-digit number)

88590736462998242224…60824711510416752639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.859 × 10⁹⁵(96-digit number)

88590736462998242224…60824711510416752641

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

1.771 × 10⁹⁶(97-digit number)

17718147292599648444…21649423020833505279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.771 × 10⁹⁶(97-digit number)

17718147292599648444…21649423020833505281

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 #2,099,981

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