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Block #97,211

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/4/2013, 2:32:10 PM Β· Difficulty 9.2982 Β· 6,727,402 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a11799ec7147bc5bc5774765f0d6b0b6b3cf38187759b5decbed7b3b702bb2ed
View on Chainz β†—

Height

#97,211

Difficulty

9.298208

Transactions

1

Size

200 B

Version

2

Bits

094c5755

Nonce

274,920

Timestamp

8/4/2013, 2:32:10 PM

Confirmations

6,727,402

Merkle Root

d809290ec8d6aa80feedc17e17b915ee6fbf5ea6f86b3006b19836fb6e26ebc4
Transactions (1)
Coinbased809290ec8d6aa…9836fb6e26ebc4
1 in β†’ 1 out11.5500 XPM109 B
AezMwyLP…rTg7Eyfk
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.

5.625 Γ— 10⁹⁷(98-digit number)
56256968287584736850…94376791061323671080
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
5.625 Γ— 10⁹⁷(98-digit number)
56256968287584736850…94376791061323671079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.625 Γ— 10⁹⁷(98-digit number)
56256968287584736850…94376791061323671081
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
1.125 Γ— 10⁹⁸(99-digit number)
11251393657516947370…88753582122647342159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.125 Γ— 10⁹⁸(99-digit number)
11251393657516947370…88753582122647342161
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
2.250 Γ— 10⁹⁸(99-digit number)
22502787315033894740…77507164245294684319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.250 Γ— 10⁹⁸(99-digit number)
22502787315033894740…77507164245294684321
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
4.500 Γ— 10⁹⁸(99-digit number)
45005574630067789480…55014328490589368639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.500 Γ— 10⁹⁸(99-digit number)
45005574630067789480…55014328490589368641
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
9.001 Γ— 10⁹⁸(99-digit number)
90011149260135578960…10028656981178737279
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 97211

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 a11799ec7147bc5bc5774765f0d6b0b6b3cf38187759b5decbed7b3b702bb2ed

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 #97,211 on Chainz β†—
Circulating Supply:57,840,964 XPMΒ·at block #6,824,612 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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