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Block #567,664

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/29/2014, 9:20:53 PM Β· Difficulty 10.9650 Β· 6,243,943 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5ebf359712f2303d5adf00a659eaa26ed8b2d3536bcc10cbf6e77867fe8d2bf6
View on Chainz β†—

Height

#567,664

Difficulty

10.964957

Transactions

1

Size

207 B

Version

2

Bits

0af70764

Nonce

131,727,787

Timestamp

5/29/2014, 9:20:53 PM

Confirmations

6,243,943

Merkle Root

eeed587a53a341566794847819488d8ed8f257e6ba2a562996fe8c3c2ab02e34
Transactions (1)
Coinbaseeeed587a53a341…fe8c3c2ab02e34
1 in β†’ 1 out8.3000 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.

7.647 Γ— 10⁹⁢(97-digit number)
76471106125274578246…45663217663315105600
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
7.647 Γ— 10⁹⁢(97-digit number)
76471106125274578246…45663217663315105599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.647 Γ— 10⁹⁢(97-digit number)
76471106125274578246…45663217663315105601
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
1.529 Γ— 10⁹⁷(98-digit number)
15294221225054915649…91326435326630211199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.529 Γ— 10⁹⁷(98-digit number)
15294221225054915649…91326435326630211201
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
3.058 Γ— 10⁹⁷(98-digit number)
30588442450109831298…82652870653260422399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.058 Γ— 10⁹⁷(98-digit number)
30588442450109831298…82652870653260422401
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
6.117 Γ— 10⁹⁷(98-digit number)
61176884900219662596…65305741306520844799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.117 Γ— 10⁹⁷(98-digit number)
61176884900219662596…65305741306520844801
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
1.223 Γ— 10⁹⁸(99-digit number)
12235376980043932519…30611482613041689599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.223 Γ— 10⁹⁸(99-digit number)
12235376980043932519…30611482613041689601
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
2.447 Γ— 10⁹⁸(99-digit number)
24470753960087865038…61222965226083379199
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 567664

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 5ebf359712f2303d5adf00a659eaa26ed8b2d3536bcc10cbf6e77867fe8d2bf6

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 #567,664 on Chainz β†—
Circulating Supply:57,736,969 XPMΒ·at block #6,811,606 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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