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Block #132,797

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/25/2013, 3:33:28 AM Β· Difficulty 9.7907 Β· 6,693,987 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c825a35272f9d5abb378f4648d9e55ee3b3b5739492061e0813bfd2b79d46238
View on Chainz β†—

Height

#132,797

Difficulty

9.790748

Transactions

1

Size

198 B

Version

2

Bits

09ca6e76

Nonce

286,867

Timestamp

8/25/2013, 3:33:28 AM

Confirmations

6,693,987

Merkle Root

a3a5868b639e4d195bf2a18f232962dbda5428b606573bd06ecd5a5ea8580fb0
Transactions (1)
Coinbasea3a5868b639e4d…cd5a5ea8580fb0
1 in β†’ 1 out10.4200 XPM109 B
Aexc4U5C…VzkLuBQ9
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.740 Γ— 10⁹¹(92-digit number)
27401147455082899620…01170200403458613760
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
2.740 Γ— 10⁹¹(92-digit number)
27401147455082899620…01170200403458613759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.740 Γ— 10⁹¹(92-digit number)
27401147455082899620…01170200403458613761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
5.480 Γ— 10⁹¹(92-digit number)
54802294910165799240…02340400806917227519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.480 Γ— 10⁹¹(92-digit number)
54802294910165799240…02340400806917227521
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.096 Γ— 10⁹²(93-digit number)
10960458982033159848…04680801613834455039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.096 Γ— 10⁹²(93-digit number)
10960458982033159848…04680801613834455041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
2.192 Γ— 10⁹²(93-digit number)
21920917964066319696…09361603227668910079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.192 Γ— 10⁹²(93-digit number)
21920917964066319696…09361603227668910081
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
4.384 Γ— 10⁹²(93-digit number)
43841835928132639392…18723206455337820159
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” 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 β†’
β˜…β˜†β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 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 132797

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 c825a35272f9d5abb378f4648d9e55ee3b3b5739492061e0813bfd2b79d46238

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 β†’ Debug Window β†’ 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 #132,797 on Chainz β†—
Circulating Supply:57,858,432 XPMΒ·at block #6,826,783 Β· updates every 60s
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