Block #2,117,121

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/15/2017, 8:15:27 AM · Difficulty 10.9051 · 4,697,323 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

17e341e1fe3346648d781df5a89132f063955ebd984a95a33c9d488bae694a61

View on Chainz ↗

Height

#2,117,121

Difficulty

10.905106

Transactions

Size

25.01 KB

Version

Bits

0ae7b506

Nonce

156,160,555

Timestamp

5/15/2017, 8:15:27 AM

Confirmations

4,697,323

Mined by

⛏️ P2SHALaTmiv9QrNPk43QwvtWHZ8t76Hwb1PoJ4

Merkle Root

7f3af00cbd578f8c01e3009ab317d3b7c346ace5e0542f3caf73c56f4884a635

Transactions (3)

Coinbase48b9ddc8241621…dc2dbf08058f6c

1 in → 1 out8.7000 XPM109 B

ALaTmiv9…Hwb1PoJ4

3a649c9d6fa812…6120c08a95741e

3 in → 1 out4817.0000 XPM487 B

ANuaV5wW…VFULZ6iV

1da0de9e821f42…5179eb7be50fb9

168 in → 2 out20.0100 XPM24.34 KB

Ae4KgVrn…uf5UDRi5 Ac9S5hBu…Kq8nGfui

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.

5.736 × 10⁹⁵(96-digit number)

57362863447228915394…04125466719213351679

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

5.736 × 10⁹⁵(96-digit number)

57362863447228915394…04125466719213351679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.736 × 10⁹⁵(96-digit number)

57362863447228915394…04125466719213351681

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

1.147 × 10⁹⁶(97-digit number)

11472572689445783078…08250933438426703359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.147 × 10⁹⁶(97-digit number)

11472572689445783078…08250933438426703361

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

2.294 × 10⁹⁶(97-digit number)

22945145378891566157…16501866876853406719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.294 × 10⁹⁶(97-digit number)

22945145378891566157…16501866876853406721

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

4.589 × 10⁹⁶(97-digit number)

45890290757783132315…33003733753706813439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.589 × 10⁹⁶(97-digit number)

45890290757783132315…33003733753706813441

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

9.178 × 10⁹⁶(97-digit number)

91780581515566264631…66007467507413626879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.178 × 10⁹⁶(97-digit number)

91780581515566264631…66007467507413626881

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 #2,117,121

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