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Block #1,258,166

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/28/2015, 7:06:14 PM · Difficulty 10.8086 · 5,586,715 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c0c5cd66c108c42443ec23c0eadd1aa8c928d7086eb730b903939e61c6b526b5

View on Chainz ↗

Height

#1,258,166

Difficulty

10.808560

Transactions

Size

1.52 KB

Version

Bits

0acefdcd

Nonce

395,195,915

Timestamp

9/28/2015, 7:06:14 PM

Confirmations

5,586,715

Merkle Root

47caf2eca93f105c52dc679030eb257eaa37731a317bc11f1dc5691541170c50

Transactions (2)

Coinbase017f51d8316f9e…c0942a1a9f83db

1 in → 1 out8.5700 XPM110 B

ANk7HbDq…y4batnKP

f2e25569b8c7ed…d2ad320134bf34

4 in → 22 out0.7095 XPM1.32 KB

ALSMi9Ex…AjRAw5aa AP4dUpdC…ikDNhBdB AWTeDHEw…EJ1nonJ2 AT9ngrHa…L1nnNKSX AGJaSRJJ…UU3puP1y

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.

8.763 × 10⁹⁷(98-digit number)

87639459411537725593…07829596343393812480

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

8.763 × 10⁹⁷(98-digit number)

87639459411537725593…07829596343393812479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.763 × 10⁹⁷(98-digit number)

87639459411537725593…07829596343393812481

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

1.752 × 10⁹⁸(99-digit number)

17527891882307545118…15659192686787624959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.752 × 10⁹⁸(99-digit number)

17527891882307545118…15659192686787624961

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

3.505 × 10⁹⁸(99-digit number)

35055783764615090237…31318385373575249919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.505 × 10⁹⁸(99-digit number)

35055783764615090237…31318385373575249921

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

7.011 × 10⁹⁸(99-digit number)

70111567529230180474…62636770747150499839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.011 × 10⁹⁸(99-digit number)

70111567529230180474…62636770747150499841

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

1.402 × 10⁹⁹(100-digit number)

14022313505846036094…25273541494300999679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.402 × 10⁹⁹(100-digit number)

14022313505846036094…25273541494300999681

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 1258166

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 c0c5cd66c108c42443ec23c0eadd1aa8c928d7086eb730b903939e61c6b526b5

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 #1,258,166 on Chainz ↗

Block #1,258,166

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