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Block #315,466

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/16/2013, 12:53:54 PM Β· Difficulty 10.1013 Β· 6,487,774 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3db956599e9696fce291f95d4253b44ac63a0338a1069e363c5d2b2e20dadf3a
View on Chainz β†—

Height

#315,466

Difficulty

10.101303

Transactions

1

Size

208 B

Version

2

Bits

0a19eefa

Nonce

65,676

Timestamp

12/16/2013, 12:53:54 PM

Confirmations

6,487,774

Merkle Root

c5ca884dd9bb4ec5cf00d038de8a74be10514532fdc97ee75fb22a1ca34146ff
Transactions (1)
Coinbasec5ca884dd9bb4e…b22a1ca34146ff
1 in β†’ 1 out9.7900 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.

4.518 Γ— 10⁹⁹(100-digit number)
45186009972363377400…22433718540824790720
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
4.518 Γ— 10⁹⁹(100-digit number)
45186009972363377400…22433718540824790719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.518 Γ— 10⁹⁹(100-digit number)
45186009972363377400…22433718540824790721
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
9.037 Γ— 10⁹⁹(100-digit number)
90372019944726754801…44867437081649581439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.037 Γ— 10⁹⁹(100-digit number)
90372019944726754801…44867437081649581441
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
1.807 Γ— 10¹⁰⁰(101-digit number)
18074403988945350960…89734874163299162879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.807 Γ— 10¹⁰⁰(101-digit number)
18074403988945350960…89734874163299162881
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
3.614 Γ— 10¹⁰⁰(101-digit number)
36148807977890701920…79469748326598325759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.614 Γ— 10¹⁰⁰(101-digit number)
36148807977890701920…79469748326598325761
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
7.229 Γ— 10¹⁰⁰(101-digit number)
72297615955781403841…58939496653196651519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.229 Γ— 10¹⁰⁰(101-digit number)
72297615955781403841…58939496653196651521
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 315466

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 3db956599e9696fce291f95d4253b44ac63a0338a1069e363c5d2b2e20dadf3a

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 #315,466 on Chainz β†—
Circulating Supply:57,669,948 XPMΒ·at block #6,803,239 Β· updates every 60s
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