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Block #553,826

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/20/2014, 10:14:41 AM Β· Difficulty 10.9630 Β· 6,246,995 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7d71e08c5d200bc262669f08fd0371604b914ecb58c1b3dea694a027ff65bc42
View on Chainz β†—

Height

#553,826

Difficulty

10.963008

Transactions

1

Size

208 B

Version

2

Bits

0af687b8

Nonce

249,125,719

Timestamp

5/20/2014, 10:14:41 AM

Confirmations

6,246,995

Merkle Root

e2035c42c5dbcfab13f099f6824a12612caab797704d068f5747def6cfcc3cef
Transactions (1)
Coinbasee2035c42c5dbcf…47def6cfcc3cef
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.825 Γ— 10⁹⁹(100-digit number)
18256006919380446004…26538413069582920960
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
1.825 Γ— 10⁹⁹(100-digit number)
18256006919380446004…26538413069582920959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.825 Γ— 10⁹⁹(100-digit number)
18256006919380446004…26538413069582920961
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
3.651 Γ— 10⁹⁹(100-digit number)
36512013838760892008…53076826139165841919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.651 Γ— 10⁹⁹(100-digit number)
36512013838760892008…53076826139165841921
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
7.302 Γ— 10⁹⁹(100-digit number)
73024027677521784017…06153652278331683839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.302 Γ— 10⁹⁹(100-digit number)
73024027677521784017…06153652278331683841
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
1.460 Γ— 10¹⁰⁰(101-digit number)
14604805535504356803…12307304556663367679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.460 Γ— 10¹⁰⁰(101-digit number)
14604805535504356803…12307304556663367681
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
2.920 Γ— 10¹⁰⁰(101-digit number)
29209611071008713606…24614609113326735359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.920 Γ— 10¹⁰⁰(101-digit number)
29209611071008713606…24614609113326735361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
5.841 Γ— 10¹⁰⁰(101-digit number)
58419222142017427213…49229218226653470719
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 553826

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 7d71e08c5d200bc262669f08fd0371604b914ecb58c1b3dea694a027ff65bc42

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 #553,826 on Chainz β†—
Circulating Supply:57,650,624 XPMΒ·at block #6,800,820 Β· updates every 60s
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