Block #2,074,231

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/17/2017, 10:26:37 AM · Difficulty 10.8360 · 4,767,742 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0bb6d019a95932aa91d173448001ddace88c3bd36963e66afb5f91fad50a417d

View on Chainz ↗

Height

#2,074,231

Difficulty

10.836008

Transactions

Size

427 B

Version

Bits

0ad60497

Nonce

461,177,364

Timestamp

4/17/2017, 10:26:37 AM

Confirmations

4,767,742

Mined by

⛏️ P2SHAQhYQnjKbpBjoVry82tetwZxb5gwdZtnZr

Merkle Root

79f7c55f6f573473903bf6ce4918a69d42876e3b8379fbadd78069a8712b61b0

Transactions (2)

Coinbaseca61c856742303…2c023e1194546c

1 in → 1 out8.5100 XPM110 B

AQhYQnjK…gwdZtnZr

fca0ccd2a666cb…bd3a8fc8d7c995

1 in → 2 out69.0571 XPM226 B

AG2H7eYT…gBGPJKfF AeAGYg7U…5efhZiSU

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.

1.977 × 10⁹⁷(98-digit number)

19778670748787126479…69890643144620031999

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

1.977 × 10⁹⁷(98-digit number)

19778670748787126479…69890643144620031999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.977 × 10⁹⁷(98-digit number)

19778670748787126479…69890643144620032001

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

3.955 × 10⁹⁷(98-digit number)

39557341497574252959…39781286289240063999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.955 × 10⁹⁷(98-digit number)

39557341497574252959…39781286289240064001

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

7.911 × 10⁹⁷(98-digit number)

79114682995148505918…79562572578480127999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.911 × 10⁹⁷(98-digit number)

79114682995148505918…79562572578480128001

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

1.582 × 10⁹⁸(99-digit number)

15822936599029701183…59125145156960255999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.582 × 10⁹⁸(99-digit number)

15822936599029701183…59125145156960256001

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

3.164 × 10⁹⁸(99-digit number)

31645873198059402367…18250290313920511999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.164 × 10⁹⁸(99-digit number)

31645873198059402367…18250290313920512001

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 #2,074,231

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