Block #2,269,594

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/27/2017, 1:24:34 AM · Difficulty 10.9525 · 4,555,751 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

91dfe9c3007cc03b1f8409374ef8cfd2e2e2f0afe42543b606a23f89ff3fd2f7

View on Chainz ↗

Height

#2,269,594

Difficulty

10.952532

Transactions

Size

2.41 KB

Version

Bits

0af3d91d

Nonce

606,336,795

Timestamp

8/27/2017, 1:24:34 AM

Confirmations

4,555,751

Mined by

⛏️ P2SHAJUjkGWE2MYdtoF7SbDHUvquXDE8nSEh2a

Merkle Root

0cd4e4ae20ce52d9298a8c0e3961306e8e5dfaa3245d72c8e9cd0cdc307e2554

Transactions (3)

Coinbase7a3272d043bbec…ded514592a05f4

1 in → 1 out8.3600 XPM109 B

AJUjkGWE…E8nSEh2a

7b402b0750290e…9f960ab4bf5049

6 in → 3 out3159.5855 XPM1001 B

ASnzm9S9…A3PBVhJE AX2cXYWN…PbYms68v ALgxzFP7…JkXTt8HL

02aa0eca80f23e…c30d7d90381228

8 in → 2 out431.0330 XPM1.23 KB

AcdKsKpw…JuBnPMRb AWVBJzri…1sMkuo1y

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.

2.216 × 10⁹⁶(97-digit number)

22165164048773491042…03997768547687137279

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

2.216 × 10⁹⁶(97-digit number)

22165164048773491042…03997768547687137279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.216 × 10⁹⁶(97-digit number)

22165164048773491042…03997768547687137281

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

4.433 × 10⁹⁶(97-digit number)

44330328097546982085…07995537095374274559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.433 × 10⁹⁶(97-digit number)

44330328097546982085…07995537095374274561

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

8.866 × 10⁹⁶(97-digit number)

88660656195093964171…15991074190748549119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.866 × 10⁹⁶(97-digit number)

88660656195093964171…15991074190748549121

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

1.773 × 10⁹⁷(98-digit number)

17732131239018792834…31982148381497098239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.773 × 10⁹⁷(98-digit number)

17732131239018792834…31982148381497098241

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

3.546 × 10⁹⁷(98-digit number)

35464262478037585668…63964296762994196479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.546 × 10⁹⁷(98-digit number)

35464262478037585668…63964296762994196481

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 #2,269,594

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