Block #2,205,937

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/14/2017, 4:05:06 AM · Difficulty 10.9460 · 4,636,194 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b02e049b06f51582609ad4a2d3ca9b7548032fc9b7926c653df3f3906e4d74c3

View on Chainz ↗

Height

#2,205,937

Difficulty

10.946030

Transactions

Size

618 B

Version

Bits

0af22f0a

Nonce

1,052,870,916

Timestamp

7/14/2017, 4:05:06 AM

Confirmations

4,636,194

Mined by

⛏️ P2SHALMvHFmrTQLUxBCXWVYT4Fwc9f3qvNzyok

Merkle Root

096b32748e47be9aa18d027ca38d8923a5465612c4a51ae18c2f0543a1a34780

Transactions (3)

Coinbasea7be86d6c23699…b4517d7b28b992

1 in → 1 out8.3500 XPM110 B

ALMvHFmr…3qvNzyok

aed9339f983276…2a679cfc7f43b4

1 in → 2 out8.3200 XPM191 B

AJ3Xt8fo…UvccZENx AKDHX5A5…mc1GDnW5

cbe570bc9d14a6…c9ab218443808e

1 in → 2 out4.3100 XPM226 B

AcSU6GUu…DD2xpjgX AKVSE3co…BT4a2S8h

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.

1.078 × 10⁹⁶(97-digit number)

10782213140446315486…09785774692213637119

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

1.078 × 10⁹⁶(97-digit number)

10782213140446315486…09785774692213637119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.078 × 10⁹⁶(97-digit number)

10782213140446315486…09785774692213637121

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

2.156 × 10⁹⁶(97-digit number)

21564426280892630973…19571549384427274239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.156 × 10⁹⁶(97-digit number)

21564426280892630973…19571549384427274241

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

4.312 × 10⁹⁶(97-digit number)

43128852561785261947…39143098768854548479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.312 × 10⁹⁶(97-digit number)

43128852561785261947…39143098768854548481

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

8.625 × 10⁹⁶(97-digit number)

86257705123570523894…78286197537709096959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.625 × 10⁹⁶(97-digit number)

86257705123570523894…78286197537709096961

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

1.725 × 10⁹⁷(98-digit number)

17251541024714104778…56572395075418193919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.725 × 10⁹⁷(98-digit number)

17251541024714104778…56572395075418193921

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 #2,205,937

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