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Block #214,723

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/17/2013, 3:57:11 PM Β· Difficulty 9.9240 Β· 6,587,778 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0d5e68bc5bf17f04bf6c34703bfe8fb23a2f13d3d1fdb1ee8a8d3ac8761a985e
View on Chainz β†—

Height

#214,723

Difficulty

9.924020

Transactions

2

Size

2.87 KB

Version

2

Bits

09ec8c93

Nonce

9,299

Timestamp

10/17/2013, 3:57:11 PM

Confirmations

6,587,778

Mined by

⛏️ P2SHAS8x3sDwFxX9uW8vM1GqQVXMegf55dw6cM

Merkle Root

1c640d7303a096238e0d8ca8a0b20a98c7a5470b325422222a91e64dcc373a1f
Transactions (2)
Coinbase0dda57b53bee06…f5734c494c2f52
1 in β†’ 1 out10.1700 XPM109 B
AS8x3sDw…f55dw6cM
e88d40a5c6ad44…93b404d32644a8
18 in β†’ 2 out8.4382 XPM2.68 KB
AVj6DQKW…1SSSyYjxAMyK1rVd…9RBG9Tb4
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.

1.460 Γ— 10⁹⁡(96-digit number)
14606900754807635755…18592179345219934719
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
1.460 Γ— 10⁹⁡(96-digit number)
14606900754807635755…18592179345219934719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.460 Γ— 10⁹⁡(96-digit number)
14606900754807635755…18592179345219934721
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
2.921 Γ— 10⁹⁡(96-digit number)
29213801509615271510…37184358690439869439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.921 Γ— 10⁹⁡(96-digit number)
29213801509615271510…37184358690439869441
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
5.842 Γ— 10⁹⁡(96-digit number)
58427603019230543021…74368717380879738879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.842 Γ— 10⁹⁡(96-digit number)
58427603019230543021…74368717380879738881
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
1.168 Γ— 10⁹⁢(97-digit number)
11685520603846108604…48737434761759477759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.168 Γ— 10⁹⁢(97-digit number)
11685520603846108604…48737434761759477761
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
2.337 Γ— 10⁹⁢(97-digit number)
23371041207692217208…97474869523518955519
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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
Cross-reference on Chainz Explorer
Circulating Supply:57,664,016 XPMΒ·at block #6,802,500 Β· updates every 60s
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