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Block #28,508

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/13/2013, 12:29:57 PM Β· Difficulty 7.9821 Β· 6,771,908 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fdf9714af3206c873ca17f976b029deec8af97843abc0f9ae681be08b002503e
View on Chainz β†—

Height

#28,508

Difficulty

7.982132

Transactions

1

Size

202 B

Version

2

Bits

07fb6d00

Nonce

197

Timestamp

7/13/2013, 12:29:57 PM

Confirmations

6,771,908

Merkle Root

b02cbdfaa80685aad29714bb6475ce1e421fdadedc93a218033f9bc71ceec869
Transactions (1)
Coinbaseb02cbdfaa80685…3f9bc71ceec869
1 in β†’ 1 out15.6700 XPM108 B
AJX7Nyni…WCZt7ReY
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.

7.651 Γ— 10¹⁰⁴(105-digit number)
76514256919662164687…38946662792015765680
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
7.651 Γ— 10¹⁰⁴(105-digit number)
76514256919662164687…38946662792015765679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.651 Γ— 10¹⁰⁴(105-digit number)
76514256919662164687…38946662792015765681
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
1.530 Γ— 10¹⁰⁡(106-digit number)
15302851383932432937…77893325584031531359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.530 Γ— 10¹⁰⁡(106-digit number)
15302851383932432937…77893325584031531361
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
3.060 Γ— 10¹⁰⁡(106-digit number)
30605702767864865875…55786651168063062719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.060 Γ— 10¹⁰⁡(106-digit number)
30605702767864865875…55786651168063062721
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
6.121 Γ— 10¹⁰⁡(106-digit number)
61211405535729731750…11573302336126125439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.121 Γ— 10¹⁰⁡(106-digit number)
61211405535729731750…11573302336126125441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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 8
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 28508

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 fdf9714af3206c873ca17f976b029deec8af97843abc0f9ae681be08b002503e

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 #28,508 on Chainz β†—
Circulating Supply:57,647,392 XPMΒ·at block #6,800,415 Β· updates every 60s
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