Home/Chain Registry/Block #2,772,501

Block #2,772,501

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/31/2018, 12:21:37 AM · Difficulty 11.6623 · 4,068,440 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e77e15912f5299d55f56f8056c190865d36509904d6b455c189d25f286d47951

View on Chainz ↗

Height

#2,772,501

Difficulty

11.662272

Transactions

Size

575 B

Version

Bits

0ba98aa3

Nonce

666,572,308

Timestamp

7/31/2018, 12:21:37 AM

Confirmations

4,068,440

Merkle Root

6df8e706c9748a8426ec6db49939811545176a3373bc9a3466d5a4fb47fbbe83

Transactions (2)

Coinbased1c3a090e8a8f8…5f87991a4d8d24

1 in → 1 out7.3500 XPM110 B

Aekq2nJR…gihtgrWv

4575890e783598…9cffddcb75bc8b

2 in → 2 out0.1218 XPM373 B

AXBGncZh…EtZN8mu8 AN7b55gz…YroqkbjU

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.

8.338 × 10⁹⁸(99-digit number)

83385076217690570876…50111004868939612160

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

8.338 × 10⁹⁸(99-digit number)

83385076217690570876…50111004868939612159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.338 × 10⁹⁸(99-digit number)

83385076217690570876…50111004868939612161

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

1.667 × 10⁹⁹(100-digit number)

16677015243538114175…00222009737879224319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.667 × 10⁹⁹(100-digit number)

16677015243538114175…00222009737879224321

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

3.335 × 10⁹⁹(100-digit number)

33354030487076228350…00444019475758448639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.335 × 10⁹⁹(100-digit number)

33354030487076228350…00444019475758448641

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

6.670 × 10⁹⁹(100-digit number)

66708060974152456701…00888038951516897279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.670 × 10⁹⁹(100-digit number)

66708060974152456701…00888038951516897281

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

1.334 × 10¹⁰⁰(101-digit number)

13341612194830491340…01776077903033794559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.334 × 10¹⁰⁰(101-digit number)

13341612194830491340…01776077903033794561

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

2.668 × 10¹⁰⁰(101-digit number)

26683224389660982680…03552155806067589119

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 2772501

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 e77e15912f5299d55f56f8056c190865d36509904d6b455c189d25f286d47951

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 #2,772,501 on Chainz ↗

Block #2,772,501

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