Block #2,110,106

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/10/2017, 1:51:40 PM · Difficulty 10.9020 · 4,729,084 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d34e6529dbde0c5b517111ae9ec13de7020c3adafc77c530a5c549ba50d5e439

View on Chainz ↗

Height

#2,110,106

Difficulty

10.901966

Transactions

Size

573 B

Version

Bits

0ae6e746

Nonce

839,077,621

Timestamp

5/10/2017, 1:51:40 PM

Confirmations

4,729,084

Mined by

⛏️ P2SHAXiF8jxBN76HvPCypaUFzsyfLhSEJfmX6s

Merkle Root

1964d518abe27c9f7d210477276b439fbbc4d85bff4776aeaa8f1b8e5b0b71ac

Transactions (2)

Coinbase9b90473a6d23f2…f6957a7f2701b6

1 in → 1 out8.4100 XPM109 B

AXiF8jxB…SEJfmX6s

ebfb5d871e49dc…46e96adf8c081f

2 in → 2 out2340.7336 XPM374 B

AM4eKV6h…jdwxcnRy AKQJUnwV…mgLMEfah

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.

8.172 × 10⁹⁴(95-digit number)

81725664472535825386…03702750654058516479

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

8.172 × 10⁹⁴(95-digit number)

81725664472535825386…03702750654058516479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.172 × 10⁹⁴(95-digit number)

81725664472535825386…03702750654058516481

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

1.634 × 10⁹⁵(96-digit number)

16345132894507165077…07405501308117032959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.634 × 10⁹⁵(96-digit number)

16345132894507165077…07405501308117032961

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

3.269 × 10⁹⁵(96-digit number)

32690265789014330154…14811002616234065919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.269 × 10⁹⁵(96-digit number)

32690265789014330154…14811002616234065921

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

6.538 × 10⁹⁵(96-digit number)

65380531578028660309…29622005232468131839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.538 × 10⁹⁵(96-digit number)

65380531578028660309…29622005232468131841

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

1.307 × 10⁹⁶(97-digit number)

13076106315605732061…59244010464936263679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.307 × 10⁹⁶(97-digit number)

13076106315605732061…59244010464936263681

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 #2,110,106

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