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Block #299,256

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/7/2013, 8:42:04 PM Β· Difficulty 9.9921 Β· 6,513,174 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7befba6026187e8d48d1e181d04fb1007d3f3a2ec7f98f3005c8304709d7d338
View on Chainz β†—

Height

#299,256

Difficulty

9.992075

Transactions

1

Size

206 B

Version

2

Bits

09fdf89b

Nonce

83,270

Timestamp

12/7/2013, 8:42:04 PM

Confirmations

6,513,174

Merkle Root

a599cea414f8f66cb38ce10d9fddcb3f84fc02fbcf7be163206f32064d70f31a
Transactions (1)
Coinbasea599cea414f8f6…6f32064d70f31a
1 in β†’ 1 out10.0000 XPM116 B
AbwWkWZt…kawDhufa
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.

7.281 Γ— 10⁹⁴(95-digit number)
72811299482595862022…96403616787034777600
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
7.281 Γ— 10⁹⁴(95-digit number)
72811299482595862022…96403616787034777599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.281 Γ— 10⁹⁴(95-digit number)
72811299482595862022…96403616787034777601
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
1.456 Γ— 10⁹⁡(96-digit number)
14562259896519172404…92807233574069555199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.456 Γ— 10⁹⁡(96-digit number)
14562259896519172404…92807233574069555201
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
2.912 Γ— 10⁹⁡(96-digit number)
29124519793038344809…85614467148139110399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.912 Γ— 10⁹⁡(96-digit number)
29124519793038344809…85614467148139110401
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
5.824 Γ— 10⁹⁡(96-digit number)
58249039586076689618…71228934296278220799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.824 Γ— 10⁹⁡(96-digit number)
58249039586076689618…71228934296278220801
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
1.164 Γ— 10⁹⁢(97-digit number)
11649807917215337923…42457868592556441599
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 299256

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 7befba6026187e8d48d1e181d04fb1007d3f3a2ec7f98f3005c8304709d7d338

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 #299,256 on Chainz β†—
Circulating Supply:57,743,462 XPMΒ·at block #6,812,429 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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