Block #2,111,017

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/11/2017, 3:49:17 AM · Difficulty 10.9035 · 4,727,736 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

20c8fdc9004e7b8a92860a89781ad6b1019c42d1aa91c250f55b8bf0e351acbf

View on Chainz ↗

Height

#2,111,017

Difficulty

10.903462

Transactions

Size

1.66 KB

Version

Bits

0ae74948

Nonce

259,042,189

Timestamp

5/11/2017, 3:49:17 AM

Confirmations

4,727,736

Mined by

⛏️ P2SHAX2ffPz6pyXoUqEuJKXeFC8CcQi26WbcQq

Merkle Root

dcf5f242db90b3d1be64143677d501a8ef968f21fcc35cbdaf04b951e968dd68

Transactions (5)

Coinbase2bc4dad57713e0…b22c4cc1ec4b82

1 in → 1 out8.4400 XPM110 B

AX2ffPz6…i26WbcQq

0103726b4def42…1fa179ec35746e

1 in → 2 out72894.3878 XPM226 B

AeRgSsvr…AjRpxd5D ASY9s79y…HKVuNbcf

2420c89747a311…4a882077a05ed7

1 in → 2 out20637.0421 XPM226 B

ATjeKjRU…dEVNyPPF Adx6AY9i…1kp4eo5X

9d2969999dad2a…cfc2007d1d7cf7

5 in → 2 out4.3407 XPM816 B

AJG7CUuX…NLT3RPDB Af3UTtDP…DumgrPkC

5c09cea1f5a91c…98bff6aa8ad626

1 in → 2 out19427.2521 XPM226 B

AYyS6v3z…gm7Ya22h AMELnVh2…H33YEG9K

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.

1.046 × 10⁹⁶(97-digit number)

10463394156806392184…07335658135290757119

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

1.046 × 10⁹⁶(97-digit number)

10463394156806392184…07335658135290757119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.046 × 10⁹⁶(97-digit number)

10463394156806392184…07335658135290757121

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

2.092 × 10⁹⁶(97-digit number)

20926788313612784369…14671316270581514239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.092 × 10⁹⁶(97-digit number)

20926788313612784369…14671316270581514241

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

4.185 × 10⁹⁶(97-digit number)

41853576627225568739…29342632541163028479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.185 × 10⁹⁶(97-digit number)

41853576627225568739…29342632541163028481

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

8.370 × 10⁹⁶(97-digit number)

83707153254451137478…58685265082326056959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.370 × 10⁹⁶(97-digit number)

83707153254451137478…58685265082326056961

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

1.674 × 10⁹⁷(98-digit number)

16741430650890227495…17370530164652113919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.674 × 10⁹⁷(98-digit number)

16741430650890227495…17370530164652113921

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 #2,111,017

Cookie Preferences