Block #2,104,526

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/7/2017, 9:51:11 AM · Difficulty 10.8798 · 4,726,766 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

89aceba8274ac468c71995ba75958598010a1fb32283e6245ff7ba328b06d49c

View on Chainz ↗

Height

#2,104,526

Difficulty

10.879790

Transactions

Size

2.14 KB

Version

Bits

0ae139f0

Nonce

28,875,230

Timestamp

5/7/2017, 9:51:11 AM

Confirmations

4,726,766

Mined by

⛏️ P2SHAYdtq9SmsCj7fs7brvFJfFo1AHyY9isHVb

Merkle Root

6e41e843c1f65d838bb023e5eaf282649ec5fb281e7baa1151dcc7d0d9f10598

Transactions (2)

Coinbasee8d7e8d552518a…5e6c0e9a568033

1 in → 1 out8.4500 XPM109 B

AYdtq9Sm…yY9isHVb

72135c3361b863…e29e5e20538081

13 in → 2 out0.7310 XPM1.95 KB

AJygiUAJ…tAaKfo3i AGhCBt9y…5YbZhydA

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.

7.181 × 10⁹¹(92-digit number)

71815723206294062420…95296289799641232199

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

7.181 × 10⁹¹(92-digit number)

71815723206294062420…95296289799641232199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.181 × 10⁹¹(92-digit number)

71815723206294062420…95296289799641232201

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

1.436 × 10⁹²(93-digit number)

14363144641258812484…90592579599282464399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.436 × 10⁹²(93-digit number)

14363144641258812484…90592579599282464401

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

2.872 × 10⁹²(93-digit number)

28726289282517624968…81185159198564928799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.872 × 10⁹²(93-digit number)

28726289282517624968…81185159198564928801

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

5.745 × 10⁹²(93-digit number)

57452578565035249936…62370318397129857599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.745 × 10⁹²(93-digit number)

57452578565035249936…62370318397129857601

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

1.149 × 10⁹³(94-digit number)

11490515713007049987…24740636794259715199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.149 × 10⁹³(94-digit number)

11490515713007049987…24740636794259715201

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 #2,104,526

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