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Block #1,171,355

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/26/2015, 1:50:35 PM · Difficulty 10.9367 · 5,670,818 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

143caf3e9e9a09bcf4abd13d2371ed9f6a5755098b543f36253f4df775effdca

View on Chainz ↗

Height

#1,171,355

Difficulty

10.936655

Transactions

Size

892 B

Version

Bits

0aefc89f

Nonce

134,209,384

Timestamp

7/26/2015, 1:50:35 PM

Confirmations

5,670,818

Merkle Root

982c033c1aaf7cc68b6218b1d81152a8fa880b63e833343ee14185a820277420

Transactions (4)

Coinbase3bf14f5fc286f5…93ee1527018b01

1 in → 1 out8.3800 XPM110 B

AGEtbety…rRyWFyva

2608158ffff440…0a3bcd53efb0f3

2 in → 2 out16.7000 XPM307 B

APpgAKn6…x32zQmKq AdGFnV3a…o6n2zX3x

38a410371a48d4…40486508aeaf40

1 in → 2 out8.3400 XPM192 B

AL1frY77…4kmovkXM AdK3ftsM…fsz6769E

9e18afc8916094…8ef69f6ac71e0b

1 in → 2 out8.3400 XPM192 B

AK1NDxY3…JdiUg22k Ad3cyAfd…YjDvHqH6

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.

6.984 × 10⁹⁶(97-digit number)

69841200621815847875…03370217840725196800

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

6.984 × 10⁹⁶(97-digit number)

69841200621815847875…03370217840725196799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.984 × 10⁹⁶(97-digit number)

69841200621815847875…03370217840725196801

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

1.396 × 10⁹⁷(98-digit number)

13968240124363169575…06740435681450393599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.396 × 10⁹⁷(98-digit number)

13968240124363169575…06740435681450393601

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

2.793 × 10⁹⁷(98-digit number)

27936480248726339150…13480871362900787199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.793 × 10⁹⁷(98-digit number)

27936480248726339150…13480871362900787201

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

5.587 × 10⁹⁷(98-digit number)

55872960497452678300…26961742725801574399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.587 × 10⁹⁷(98-digit number)

55872960497452678300…26961742725801574401

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

1.117 × 10⁹⁸(99-digit number)

11174592099490535660…53923485451603148799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.117 × 10⁹⁸(99-digit number)

11174592099490535660…53923485451603148801

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.

View full Prime Chain Discovery page →

★★☆☆☆

Rarity

UncommonChain length 10

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

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 1171355

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock 143caf3e9e9a09bcf4abd13d2371ed9f6a5755098b543f36253f4df775effdca

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #1,171,355 on Chainz ↗

Block #1,171,355

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