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Block #552,842

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/19/2014, 6:15:30 PM Β· Difficulty 10.9628 Β· 6,274,185 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
85512ce4a48c9368a3c6b4d6e9d63f5f97e988af9ce1fc3cf87d3bf62fd71ce5
View on Chainz β†—

Height

#552,842

Difficulty

10.962788

Transactions

1

Size

208 B

Version

2

Bits

0af67941

Nonce

366,356,156

Timestamp

5/19/2014, 6:15:30 PM

Confirmations

6,274,185

Merkle Root

07aa70ab550af27be0347ac21b75df5cabbf75583866c6de76288173eef7a652
Transactions (1)
Coinbase07aa70ab550af2…288173eef7a652
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.

1.929 Γ— 10⁹⁸(99-digit number)
19297368060583469157…36538914487071415720
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
1.929 Γ— 10⁹⁸(99-digit number)
19297368060583469157…36538914487071415719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.929 Γ— 10⁹⁸(99-digit number)
19297368060583469157…36538914487071415721
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
3.859 Γ— 10⁹⁸(99-digit number)
38594736121166938315…73077828974142831439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.859 Γ— 10⁹⁸(99-digit number)
38594736121166938315…73077828974142831441
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
7.718 Γ— 10⁹⁸(99-digit number)
77189472242333876631…46155657948285662879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.718 Γ— 10⁹⁸(99-digit number)
77189472242333876631…46155657948285662881
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
1.543 Γ— 10⁹⁹(100-digit number)
15437894448466775326…92311315896571325759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.543 Γ— 10⁹⁹(100-digit number)
15437894448466775326…92311315896571325761
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
3.087 Γ— 10⁹⁹(100-digit number)
30875788896933550652…84622631793142651519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.087 Γ— 10⁹⁹(100-digit number)
30875788896933550652…84622631793142651521
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
6.175 Γ— 10⁹⁹(100-digit number)
61751577793867101304…69245263586285303039
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 552842

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 85512ce4a48c9368a3c6b4d6e9d63f5f97e988af9ce1fc3cf87d3bf62fd71ce5

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 #552,842 on Chainz β†—
Circulating Supply:57,860,396 XPMΒ·at block #6,827,026 Β· updates every 60s
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