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Block #224,516

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/23/2013, 8:00:03 PM Β· Difficulty 9.9370 Β· 6,588,173 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9fe30da03271973237cc3b104f962ee3e50db8fa97cd247ad162680b9178c3f6
View on Chainz β†—

Height

#224,516

Difficulty

9.937040

Transactions

1

Size

206 B

Version

2

Bits

09efe1d7

Nonce

2,436

Timestamp

10/23/2013, 8:00:03 PM

Confirmations

6,588,173

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

42a8bd3f10b99c8962578309e878c7a0cf96fa6f23c63b0f3a53f483d4188743
Transactions (1)
Coinbase42a8bd3f10b99c…53f483d4188743
1 in β†’ 1 out10.1100 XPM116 B
AcLBm5Z9…S683d7c3
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.

6.402 Γ— 10⁹³(94-digit number)
64029674322194052903…92792266151939553599
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
6.402 Γ— 10⁹³(94-digit number)
64029674322194052903…92792266151939553599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.402 Γ— 10⁹³(94-digit number)
64029674322194052903…92792266151939553601
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
1.280 Γ— 10⁹⁴(95-digit number)
12805934864438810580…85584532303879107199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.280 Γ— 10⁹⁴(95-digit number)
12805934864438810580…85584532303879107201
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
2.561 Γ— 10⁹⁴(95-digit number)
25611869728877621161…71169064607758214399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.561 Γ— 10⁹⁴(95-digit number)
25611869728877621161…71169064607758214401
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
5.122 Γ— 10⁹⁴(95-digit number)
51223739457755242323…42338129215516428799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.122 Γ— 10⁹⁴(95-digit number)
51223739457755242323…42338129215516428801
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
1.024 Γ— 10⁹⁡(96-digit number)
10244747891551048464…84676258431032857599
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:57,745,547 XPMΒ·at block #6,812,688 Β· updates every 60s
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