Home/Chain Registry/Block #2,776,869

Block #2,776,869

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/3/2018, 2:14:51 AM · Difficulty 11.6579 · 4,060,037 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

24bc53ee1700c35f09c1a98ad98b776cfa7b5f11bdce680664f04f43b6c917c5

View on Chainz ↗

Height

#2,776,869

Difficulty

11.657869

Transactions

Size

1.21 KB

Version

Bits

0ba86a1b

Nonce

30,762,146

Timestamp

8/3/2018, 2:14:51 AM

Confirmations

4,060,037

Merkle Root

f13f8ae8246e385f314f5e1f35cac437e261e8ed2bd941806ded08d4eab60853

Transactions (3)

Coinbasecf25a1c2d97ac0…0098c78c1ddfbd

1 in → 1 out7.3700 XPM110 B

AZtxQr2F…7grUWrUz

7505c1695a7c24…7231ee25a5e500

3 in → 2 out10.6900 XPM520 B

ATEy9cxL…LgviB6pF AR3zesxx…zzhd2A3M

350dda3fbce8c7…c8c33838186f60

3 in → 2 out10.1500 XPM521 B

AaFrFAJr…WqbBDLbz AWUfbtXE…eBDeuUfT

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.

8.781 × 10⁹⁴(95-digit number)

87816240034727618146…45869671747551195840

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

8.781 × 10⁹⁴(95-digit number)

87816240034727618146…45869671747551195839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.781 × 10⁹⁴(95-digit number)

87816240034727618146…45869671747551195841

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

1.756 × 10⁹⁵(96-digit number)

17563248006945523629…91739343495102391679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.756 × 10⁹⁵(96-digit number)

17563248006945523629…91739343495102391681

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

3.512 × 10⁹⁵(96-digit number)

35126496013891047258…83478686990204783359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.512 × 10⁹⁵(96-digit number)

35126496013891047258…83478686990204783361

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

7.025 × 10⁹⁵(96-digit number)

70252992027782094517…66957373980409566719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.025 × 10⁹⁵(96-digit number)

70252992027782094517…66957373980409566721

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

1.405 × 10⁹⁶(97-digit number)

14050598405556418903…33914747960819133439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.405 × 10⁹⁶(97-digit number)

14050598405556418903…33914747960819133441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.810 × 10⁹⁶(97-digit number)

28101196811112837806…67829495921638266879

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 2776869

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 24bc53ee1700c35f09c1a98ad98b776cfa7b5f11bdce680664f04f43b6c917c5

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 #2,776,869 on Chainz ↗

Block #2,776,869

Cookie Preferences