Block #2,134,083

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/27/2017, 12:09:52 AM · Difficulty 10.9088 · 4,707,471 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a4af04c8d5b6c842f06184cbaa26972f51209e3ed5d431a3b98496784fcd1704

View on Chainz ↗

Height

#2,134,083

Difficulty

10.908753

Transactions

Size

877 B

Version

Bits

0ae8a40e

Nonce

501,937,960

Timestamp

5/27/2017, 12:09:52 AM

Confirmations

4,707,471

Mined by

⛏️ P2SHAWuv71V3cE99w2WqzQfgh6WGajdDt8KPv7

Merkle Root

6d3dab52b8efa9009f2c5aeb9c9775a2d16236194e5e47076a7d7884c1a94662

Transactions (4)

Coinbaseeaaae6fe9d011b…04462f4bcaf64d

1 in → 1 out8.4200 XPM109 B

AWuv71V3…dDt8KPv7

6af19485a5e58b…99591e8611f9f0

1 in → 2 out115585.7263 XPM226 B

APe7MFxP…LWenBVYt ATCbTezi…vwFya8Tn

0f578b3a0b323b…a26eae6cc7f38f

1 in → 2 out115573.3385 XPM226 B

ASrEhZyP…x127miwx APe7MFxP…LWenBVYt

acc3fa14364c90…70a0cffbc2f68c

1 in → 2 out113068.7159 XPM225 B

AHHiXabu…PuJRL1xN AZEZfxMr…WFcWopJv

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.

1.244 × 10⁹⁷(98-digit number)

12445358470987688405…55275208302192639999

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

1.244 × 10⁹⁷(98-digit number)

12445358470987688405…55275208302192639999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.244 × 10⁹⁷(98-digit number)

12445358470987688405…55275208302192640001

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

2.489 × 10⁹⁷(98-digit number)

24890716941975376811…10550416604385279999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.489 × 10⁹⁷(98-digit number)

24890716941975376811…10550416604385280001

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

4.978 × 10⁹⁷(98-digit number)

49781433883950753623…21100833208770559999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.978 × 10⁹⁷(98-digit number)

49781433883950753623…21100833208770560001

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

9.956 × 10⁹⁷(98-digit number)

99562867767901507246…42201666417541119999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.956 × 10⁹⁷(98-digit number)

99562867767901507246…42201666417541120001

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

1.991 × 10⁹⁸(99-digit number)

19912573553580301449…84403332835082239999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.991 × 10⁹⁸(99-digit number)

19912573553580301449…84403332835082240001

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 #2,134,083

Cookie Preferences