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Block #56,931

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/17/2013, 11:08:23 AM Β· Difficulty 8.9517 Β· 6,750,907 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2c9679379bc24aa1a7d7b7b276214bbdb26274234bb8c1be4b5136ef5b06e211
View on Chainz β†—

Height

#56,931

Difficulty

8.951682

Transactions

1

Size

201 B

Version

2

Bits

08f3a16f

Nonce

963

Timestamp

7/17/2013, 11:08:23 AM

Confirmations

6,750,907

Merkle Root

d3da16d0ff22678382d84651c278996e3efdaa70ca1ee415b0a561e57bb6f069
Transactions (1)
Coinbased3da16d0ff2267…a561e57bb6f069
1 in β†’ 1 out12.4600 XPM110 B
Acecj4WY…wKtCNbS5
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.

7.228 Γ— 10⁹⁢(97-digit number)
72284035024025234816…16303854748595564050
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
7.228 Γ— 10⁹⁢(97-digit number)
72284035024025234816…16303854748595564049
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.228 Γ— 10⁹⁢(97-digit number)
72284035024025234816…16303854748595564051
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
1.445 Γ— 10⁹⁷(98-digit number)
14456807004805046963…32607709497191128099
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.445 Γ— 10⁹⁷(98-digit number)
14456807004805046963…32607709497191128101
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
2.891 Γ— 10⁹⁷(98-digit number)
28913614009610093926…65215418994382256199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.891 Γ— 10⁹⁷(98-digit number)
28913614009610093926…65215418994382256201
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
5.782 Γ— 10⁹⁷(98-digit number)
57827228019220187853…30430837988764512399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.782 Γ— 10⁹⁷(98-digit number)
57827228019220187853…30430837988764512401
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
1.156 Γ— 10⁹⁸(99-digit number)
11565445603844037570…60861675977529024799
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 56931

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 2c9679379bc24aa1a7d7b7b276214bbdb26274234bb8c1be4b5136ef5b06e211

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 #56,931 on Chainz β†—
Circulating Supply:57,706,741 XPMΒ·at block #6,807,837 Β· updates every 60s
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