Block #2,136,187

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/28/2017, 10:36:30 PM · Difficulty 10.8956 · 4,702,947 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f0b3d6bba935ad8a74b11f43e675fdfd4f178af8f38d01415ba293b77094a44f

View on Chainz ↗

Height

#2,136,187

Difficulty

10.895615

Transactions

Size

1.94 KB

Version

Bits

0ae54705

Nonce

1,829,001,917

Timestamp

5/28/2017, 10:36:30 PM

Confirmations

4,702,947

Mined by

⛏️ P2SHAGgTTGiBfezDVWavuYXnC4TdJpyUK5MFsv

Merkle Root

56c1b73550994a325ee8fc463c212ff8b2befec70c710c8d319b027706201f7f

Transactions (5)

Coinbase3227e6aa62d836…5523d5496ba41a

1 in → 1 out8.4600 XPM109 B

AGgTTGiB…yUK5MFsv

e6b8e318011279…62d1ea6a85d6b6

5 in → 2 out2970.0145 XPM817 B

AM5iAcHi…EaSLASCq ARwbcKcQ…yrecEdME

1db4d006d35de7…3cdce0c0c63e9f

3 in → 2 out541.5200 XPM521 B

AMenvinw…ggpK6QoD ASVWHaNp…Nyr3qvcZ

4fc2f95dc957be…e9e1ccbd01fc09

1 in → 2 out188.0900 XPM224 B

AN1P1XPK…aMEHbBEm ANuk41Az…3Tx7B1PJ

0a2d191d832eea…3129967d493473

1 in → 2 out4.3642 XPM225 B

AMvy6e4r…7RqqH4sD ANCGVTkJ…8AP3sQiR

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.

1.829 × 10⁹⁸(99-digit number)

18290766351237355733…69133804791546511359

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

1.829 × 10⁹⁸(99-digit number)

18290766351237355733…69133804791546511359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.829 × 10⁹⁸(99-digit number)

18290766351237355733…69133804791546511361

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

3.658 × 10⁹⁸(99-digit number)

36581532702474711466…38267609583093022719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.658 × 10⁹⁸(99-digit number)

36581532702474711466…38267609583093022721

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

7.316 × 10⁹⁸(99-digit number)

73163065404949422933…76535219166186045439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.316 × 10⁹⁸(99-digit number)

73163065404949422933…76535219166186045441

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

1.463 × 10⁹⁹(100-digit number)

14632613080989884586…53070438332372090879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.463 × 10⁹⁹(100-digit number)

14632613080989884586…53070438332372090881

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

2.926 × 10⁹⁹(100-digit number)

29265226161979769173…06140876664744181759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.926 × 10⁹⁹(100-digit number)

29265226161979769173…06140876664744181761

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 #2,136,187

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