Block #2,116,662

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/15/2017, 1:10:51 AM · Difficulty 10.9044 · 4,726,044 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2959034d76f31f3733d8e0624f298af41a21a99c81559fc600e4120870759b0f

View on Chainz ↗

Height

#2,116,662

Difficulty

10.904427

Transactions

Size

424 B

Version

Bits

0ae7888d

Nonce

370,048,746

Timestamp

5/15/2017, 1:10:51 AM

Confirmations

4,726,044

Mined by

⛏️ P2SHAR5FDpnfKM94bSeAdjD17LHghqwYc2M516

Merkle Root

d12baf8625401f1807b58667cd472fb239fdad887ce6535e0d361ace0b9408ce

Transactions (2)

Coinbase8f6008c0fbbe2a…e1f3ab3488a3a8

1 in → 1 out8.4100 XPM110 B

AR5FDpnf…wYc2M516

47948e05c29242…e31f31481dfb2d

1 in → 2 out39.0548 XPM225 B

AUi6YKYB…DTAtvUPr AWwKXxET…gabHVYya

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.

1.027 × 10⁹²(93-digit number)

10277337465835623986…25327103832325745519

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

1.027 × 10⁹²(93-digit number)

10277337465835623986…25327103832325745519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.027 × 10⁹²(93-digit number)

10277337465835623986…25327103832325745521

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

2.055 × 10⁹²(93-digit number)

20554674931671247973…50654207664651491039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.055 × 10⁹²(93-digit number)

20554674931671247973…50654207664651491041

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

4.110 × 10⁹²(93-digit number)

41109349863342495946…01308415329302982079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.110 × 10⁹²(93-digit number)

41109349863342495946…01308415329302982081

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

8.221 × 10⁹²(93-digit number)

82218699726684991892…02616830658605964159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.221 × 10⁹²(93-digit number)

82218699726684991892…02616830658605964161

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

1.644 × 10⁹³(94-digit number)

16443739945336998378…05233661317211928319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.644 × 10⁹³(94-digit number)

16443739945336998378…05233661317211928321

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 #2,116,662

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