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Block #90,142

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/30/2013, 9:24:13 PM · Difficulty 9.2527 · 6,701,784 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

91f2470048e88ed180644bc1f3551714dd848336bb4e03e5365a64393ff4593d

View on Chainz ↗

Height

#90,142

Difficulty

9.252652

Transactions

Size

204 B

Version

Bits

0940adcc

Nonce

342,099

Timestamp

7/30/2013, 9:24:13 PM

Confirmations

6,701,784

Merkle Root

d20d509ce609627470af066574db544f967dadd6315bdce10e170c5aefaf8b98

Transactions (1)

Coinbased20d509ce60962…170c5aefaf8b98

1 in → 1 out11.6600 XPM112 B

AT5A2KL6…CT16n6i2

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.

6.886 × 10⁹⁸(99-digit number)

68866917320987046289…78423434729146579510

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

6.886 × 10⁹⁸(99-digit number)

68866917320987046289…78423434729146579509

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.886 × 10⁹⁸(99-digit number)

68866917320987046289…78423434729146579511

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

1.377 × 10⁹⁹(100-digit number)

13773383464197409257…56846869458293159019

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.377 × 10⁹⁹(100-digit number)

13773383464197409257…56846869458293159021

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

2.754 × 10⁹⁹(100-digit number)

27546766928394818515…13693738916586318039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.754 × 10⁹⁹(100-digit number)

27546766928394818515…13693738916586318041

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

5.509 × 10⁹⁹(100-digit number)

55093533856789637031…27387477833172636079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.509 × 10⁹⁹(100-digit number)

55093533856789637031…27387477833172636081

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

1.101 × 10¹⁰⁰(101-digit number)

11018706771357927406…54774955666345272159

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

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 90142

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 91f2470048e88ed180644bc1f3551714dd848336bb4e03e5365a64393ff4593d

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 #90,142 on Chainz ↗