Block #2,181,956

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/28/2017, 12:08:02 AM · Difficulty 10.9371 · 4,642,755 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9a7b719a3dbd407ef962496b6cfe705b21ad45e1c8a2619632469848c77df94e

View on Chainz ↗

Height

#2,181,956

Difficulty

10.937071

Transactions

Size

654 B

Version

Bits

0aefe3dd

Nonce

342,778,428

Timestamp

6/28/2017, 12:08:02 AM

Confirmations

4,642,755

Mined by

⛏️ P2SHAQS2UtPTKrQpKy1re8nCu7BquBahShW8go

Merkle Root

f86d39b893b11ed4373e3f7c7cdfa13a8a04d3056d03ba8b54c5c786ab9ecc9e

Transactions (3)

Coinbase12ac883c252512…a990f7fd6eaf38

1 in → 1 out8.3700 XPM110 B

AQS2UtPT…ahShW8go

14c24f5d22483a…7cfaf0b1308f2b

1 in → 2 out2633.8025 XPM226 B

AZxSv1qo…psGzapJg Act6NdQD…Pf6JLUce

0452a24cc005a1…15c19b880d728a

1 in → 2 out2347.7825 XPM227 B

AWo6LvxT…iajTXNmu AYVBmLey…e5tVN1ar

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.

6.029 × 10⁹⁷(98-digit number)

60295523392400435518…81666515230932213759

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

6.029 × 10⁹⁷(98-digit number)

60295523392400435518…81666515230932213759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.029 × 10⁹⁷(98-digit number)

60295523392400435518…81666515230932213761

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

1.205 × 10⁹⁸(99-digit number)

12059104678480087103…63333030461864427519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.205 × 10⁹⁸(99-digit number)

12059104678480087103…63333030461864427521

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

2.411 × 10⁹⁸(99-digit number)

24118209356960174207…26666060923728855039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.411 × 10⁹⁸(99-digit number)

24118209356960174207…26666060923728855041

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

4.823 × 10⁹⁸(99-digit number)

48236418713920348414…53332121847457710079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.823 × 10⁹⁸(99-digit number)

48236418713920348414…53332121847457710081

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

9.647 × 10⁹⁸(99-digit number)

96472837427840696828…06664243694915420159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.647 × 10⁹⁸(99-digit number)

96472837427840696828…06664243694915420161

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 #2,181,956

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